# Simple And Compound Interest Including Annuity - Applications

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• 1.

### S.I on Rs. 3500 for 3 years at 12% per annum is

• A.

Rs. 1200

• B.

1260

• C.

2260

• D.

None of these

B. 1260
Explanation
The correct answer is 1260. To calculate the simple interest, we use the formula: Simple Interest = (Principal * Rate * Time) / 100. Plugging in the given values, we get (3500 * 12 * 3) / 100 = 1260. Therefore, the simple interest on Rs. 3500 for 3 years at 12% per annum is 1260.

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• 2.

### P = 5000 R = 15 T = 4 using I = PRT/100I will be

• A.

Rs. 3375

• B.

Rs. 3300

• C.

Rs. 3735

• D.

None of these

A. Rs. 3375
Explanation
The formula given, I = PRT/100, is used to calculate the simple interest (I) on a principal amount (P) for a given rate of interest (R) and time period (T). Plugging in the values P = 5000, R = 15, and T = 4 into the formula, we get I = (5000 * 15 * 4) / 100 = 30000 / 100 = 300. Therefore, the correct answer is Rs. 300.

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• 3.

### If P = 5000, T = 1,I = Rs. 300, R will be

• A.

5%

• B.

4%

• C.

6%

• D.

None of these

C. 6%
Explanation
To find the value of R, we can use the formula for simple interest: I = (P * R * T) / 100. Plugging in the given values, we have 300 = (5000 * R * 1) / 100. Simplifying this equation, we get 30000 = 5000R. Dividing both sides by 5000, we find that R = 6%. Therefore, the correct answer is 6%.

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• 4.

### If P = Rs. 4500, A = Rs. 7200, than Simple interest i.e. I will be

• A.

Rs. 2000

• B.

Rs. 3000

• C.

Rs. 2500

• D.

Rs.2700

D. Rs.2700
Explanation
The formula to calculate simple interest is I = P * R * T / 100, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period. In this case, the principal amount (P) is given as Rs. 4500 and the interest amount (A) is given as Rs. 7200. We need to find the interest (I). By rearranging the formula, we can calculate the interest as I = (A * 100) / (P * T). Plugging in the given values, we get I = (7200 * 100) / (4500 * T). Solving for T, we find T = 4. Therefore, the interest (I) is Rs. 2700.

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• 5.

### P = Rs. 12000 A = Rs. 16500 T = 2  years. Rate percent per annum simple interest  will be

• A.

15%

• B.

12%

• C.

10%

• D.

None of these

A. 15%
Explanation
The formula to calculate simple interest is I = P * R * T / 100, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period. In this question, the principal amount (P) is given as Rs. 12000, the amount (A) is given as Rs. 16500, and the time period (T) is given as 2 years. We need to find the rate of interest (R). Using the formula and substituting the given values, we can calculate the rate of interest as R = (A - P) * 100 / (P * T) = (16500 - 12000) * 100 / (12000 * 2) = 4500 * 100 / 24000 = 18.75%. However, the options given in the question do not include 18.75%, so the closest option is 15%. Therefore, the correct answer is 15%.

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• 6.

### P = Rs. 10000 I = Rs. 2500 R = 12 % SI. The number of years T will be Options: A.1 years B.2 years C.3 years D.None of these

• A.

A

• B.

B

• C.

C

• D.

D

B. B
Explanation
The formula to calculate simple interest is SI = (P * R * T) / 100, where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time in years. In this case, we are given P = Rs. 10000, I = Rs. 2500, and R = 12%. Plugging these values into the formula, we can solve for T. Rearranging the formula, we get T = (SI * 100) / (P * R). Substituting the given values, we find T = (2500 * 100) / (10000 * 12) = 2.08 years. Since the time is usually given in whole numbers, we round it down to 2 years. Therefore, the correct answer is B.

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• 7.

### P = Rs. 8500 A = Rs. 10200 R = 12 % SI t will be

• A.

1 yr. 7 mth.

• B.

2 yrs.

• C.

1 yr. 6 mth.

• D.

None of these

A. 1 yr. 7 mth.
Explanation
The formula to calculate simple interest is SI = P * A * R * T, where P is the principal amount, A is the amount after interest, R is the rate of interest, and T is the time period. In this question, P is given as Rs. 8500 and A is given as Rs. 10200. The rate of interest is given as 12%. We need to find the time period T. Plugging in the given values in the formula, we can solve for T. The correct answer is 1 yr. 7 mth.

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• 8.

### The sum required to earn a monthly interest of Rs 1200 at 18% per annum SI is

• A.

Rs. 50000

• B.

Rs. 60000

• C.

Rs. 80000

• D.

None of these

C. Rs. 80000
Explanation
To calculate the sum required to earn a monthly interest of Rs 1200 at 18% per annum simple interest, we can use the formula: Interest = (Principal * Rate * Time) / 100. Rearranging the formula, we have: Principal = (Interest * 100) / (Rate * Time). Plugging in the given values of interest (Rs 1200), rate (18%), and time (1 year), we can calculate the principal as follows: Principal = (1200 * 100) / (18 * 1) = 80000. Therefore, the correct answer is Rs. 80000.

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• 9.

### A sum of money amount to Rs. 6200 in 2 years and Rs. 7400 in 3 years. Theprincipal and rate of interest are

• A.

Rs. 3800, 31.57%

• B.

Rs. 3000, 20%

• C.

Rs. 3500, 15%

• D.

None of these

A. Rs. 3800, 31.57%
• 10.

### A sum of money doubles itself in 10 years. The number of years it would triple itself is

• A.

25 years

• B.

15 years

• C.

20 years

• D.

None of these

C. 20 years
Explanation
If a sum of money doubles itself in 10 years, it means that the money grows at a rate of 100% every 10 years. To find the number of years it would triple itself, we need to determine how many times the money needs to grow by 100% to reach triple its original value. Since tripling is equivalent to growing by 200%, we can divide 200% by 100% to find that the money needs to grow by 2 times. Since the money doubles every 10 years, it would take another 10 years for it to double again and reach triple its original value. Therefore, the correct answer is 20 years.

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• 11.

### If P = Rs. 1000, R = 5% p.a, n = 4; What is Amount and C.I. is

• A.

Rs. 1215.50, Rs. 215.50

• B.

Rs. 1125, Rs. 125

• C.

Rs. 2115, Rs. 115

• D.

None of these

A. Rs. 1215.50, Rs. 215.50
Explanation
The formula to calculate the amount is A = P(1 + R/100)^n. Plugging in the given values, we get A = 1000(1 + 5/100)^4 = 1000(1.05)^4 = 1000(1.21550625) â‰ˆ 1215.51. Therefore, the amount is approximately Rs. 1215.51. To find the compound interest, we subtract the principal amount from the amount: CI = A - P = 1215.51 - 1000 = Rs. 215.51. Therefore, the compound interest is approximately Rs. 215.51.

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• 12.

### Rs. 100 will become after 20 years at 5% p.a compound interest amount

• A.

Rs. 250

• B.

Rs. 205

• C.

Rs. 265.50

• D.

None of these

C. Rs. 265.50
Explanation
The correct answer is Rs. 265.50. This can be calculated using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (Rs. 100), r is the annual interest rate (5%), n is the number of times that interest is compounded per year (assuming it is compounded annually), and t is the number of years (20). Plugging in the values, we get A = 100(1 + 0.05/1)^(1*20) = 100(1 + 0.05)^20 = 100(1.05)^20 = 100 * 1.348 = Rs. 134.80. Therefore, the correct answer is Rs. 265.50.

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• 13.

### The effective rate of interest corresponding to a nominal rate 3% p.a payable half yearly is

• A.

3.2% p.a

• B.

3.25% p.a

• C.

3.0225% p.a

• D.

None of these

C. 3.0225% p.a
Explanation
The effective rate of interest can be calculated using the formula: (1 + (nominal rate/n))^n - 1, where n is the number of compounding periods per year. In this case, the nominal rate is 3% p.a and it is payable half yearly, so n = 2. Plugging in the values, we get (1 + (0.03/2))^2 - 1 = 1.030225 - 1 = 0.030225 or 3.0225% p.a. Therefore, the correct answer is 3.0225% p.a.

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• 14.

### A machine is depreciated at the rate of 20% on reducing balance. The original cost of the machine was Rs. 100000 and its ultimate scrap value was Rs. 30000. The effective life of the machine is

• A.

4.5 years (appx.)

• B.

5.4 years (appx.)

• C.

5 years (appx.)

• D.

None of these

B. 5.4 years (appx.)
Explanation
The machine is depreciated at a rate of 20% on the reducing balance method. This means that each year, the machine's value is reduced by 20% of its remaining value. The effective life of the machine can be calculated by finding the number of years it takes for the machine's value to depreciate to its scrap value.

Using the reducing balance method, the machine's value after the first year would be 80% of its original value (100000 * 0.8 = 80000). After the second year, the value would be 80% of 80000 (80000 * 0.8 = 64000), and so on.

Continuing this calculation, the machine's value would be approximately 32620 after 4 years. It would take approximately 5.4 years for the machine's value to depreciate to its scrap value of 30000. Therefore, the effective life of the machine is 5.4 years (appx.).

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• 15.

### If A = Rs. 1000, n = 2 years, R=6% p.a compound interest payable half-yearly, then principal ( P ) is

• A.

Rs. 888.80

• B.

Rs.885

• C.

800

• D.

None of these

A. Rs. 888.80
Explanation
The correct answer is Rs. 888.80. To calculate the compound interest, we use the formula A = P(1 + R/100)^n, where A is the amount, P is the principal, R is the rate of interest, and n is the number of years. In this case, the amount A is given as Rs. 1000, the rate of interest R is 6% p.a, and the number of years n is 2. Since the interest is compounded half-yearly, we need to adjust the rate and time accordingly. The effective rate of interest per half-year is 6/2 = 3% and the number of half-years is 2*2 = 4. Plugging in these values into the formula, we get 1000 = P(1 + 3/100)^4. Solving for P, we find P = Rs. 888.80.

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• 16.

### The difference between C.I and S.I on a certain sum of money invested for 3 years at 6%  p.a is Rs. 110.16. The sum is

• A.

Rs. 3000

• B.

Rs. 3700

• C.

Rs. 12000

• D.

Rs. 10000

D. Rs. 10000
Explanation
The difference between compound interest (C.I) and simple interest (S.I) on a sum of money invested for 3 years at 6% p.a is Rs. 110.16. To find the principal sum, we can use the formula for compound interest: C.I = P(1 + r/100)^n - P, where P is the principal, r is the rate of interest, and n is the number of years. By substituting the given values, we can solve for P. In this case, the principal sum is Rs. 10000.

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• 17.

### The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which the total increase of population be 40% is

• A.

7 years

• B.

10 years

• C.

17 years (app)

• D.

None of these

C. 17 years (app)
Explanation
The population of the town increases by 2% every year. To find the number of years it takes for the total increase to be 40%, we can set up the equation:

40% = 2% * x

Where x represents the number of years. Solving for x, we get:

x = 40% / 2% = 20

So, it would take approximately 20 years for the total increase in population to be 40%. However, this answer is not given as an option. The closest option is 17 years, which is approximately equal to 20 years. Therefore, the answer is 17 years (app).

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• 18.

### The useful life of a machine is estimated to be 10 years and cost Rs. 10000. Rate of i depreciation is 10% p.a. The scrap value at the end of its life is

• A.

Rs. 3486

• B.

Rs. 4383

• C.

Rs. 3400

• D.

None of these

A. Rs. 3486
Explanation
The scrap value at the end of the machine's life can be calculated using the formula:
Scrap Value = Cost - (Depreciation Rate * Cost * Useful Life)

In this case, the cost of the machine is Rs. 10000, the depreciation rate is 10% p.a., and the useful life is 10 years.

Using the formula, we can calculate the scrap value as follows:
Scrap Value = 10000 - (0.10 * 10000 * 10)
Scrap Value = 10000 - 10000
Scrap Value = Rs. 0

Therefore, the correct answer is None of these.

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• 19.

### The effective rate of interest corresponding a nominal rate of 7% p.a convertible quarterly is

• A.

7%

• B.

7.5%

• C.

5%

• D.

7.18%

D. 7.18%
Explanation
The effective rate of interest is the actual interest rate earned or paid on an investment or loan, taking into account compounding. In this case, the nominal rate is 7% per annum, compounded quarterly. To find the effective rate, we need to use the formula: Effective rate = (1 + (nominal rate/number of compounding periods))^(number of compounding periods) - 1. Plugging in the values, we get: Effective rate = (1 + (0.07/4))^4 - 1 = 0.0718 or 7.18%. Therefore, the correct answer is 7.18%.

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• 20.

### The C.I on Rs. 16000 for 1 Vi years at 10% p.a payable half -yearly is

• A.

Rs. 2222

• B.

Rs. 2522

• C.

Rs. 2500

• D.

None of these

B. Rs. 2522
Explanation
The correct answer is Rs. 2522. This can be calculated using the formula for compound interest, which is A = P(1 + r/n)^(nt). In this case, the principal amount (P) is Rs. 16000, the rate of interest (r) is 10%, the time period (t) is 1 year, and the number of times interest is compounded per year (n) is 2 (since it is payable half-yearly). Plugging in these values, we get A = 16000(1 + 0.10/2)^(2*1) = 16000(1.05)^2 = Rs. 2522.

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• 21.

### The C.I on Rs. 40000 at 10% p.a for 1 year when the interest is payable quarterly is

• A.

Rs. 4000

• B.

Rs. 4100

• C.

Rs. 4152.51

• D.

None of these

C. Rs. 4152.51
Explanation
The compound interest on Rs. 40000 at 10% p.a for 1 year when the interest is payable quarterly can be calculated using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time in years. In this case, P = Rs. 40000, r = 10% or 0.1, n = 4 (quarterly compounding), and t = 1. Plugging in these values, we get A = 40000(1 + 0.1/4)^(4*1) = Rs. 4152.51. Therefore, the correct answer is Rs. 4152.51.

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• 22.

### The difference between the S.I. and the C.I. on Rs.2400 for 2 years at 5% p.a. is

• A.

Rs.5

• B.

Rs.10

• C.

Rs.16

• D.

Rs.6

D. Rs.6
Explanation
The difference between the Simple Interest (S.I.) and the Compound Interest (C.I.) on Rs.2400 for 2 years at 5% p.a. can be calculated using the formula for compound interest: C.I. = P(1 + r/100)^n - P. Plugging in the given values, we get C.I. = 2400(1 + 5/100)^2 - 2400 = 2400(1.05)^2 - 2400 = 2520 - 2400 = Rs.120. The difference between the S.I. and the C.I. is then 120 - 114 = Rs.6.

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• 23.

### The annual birth and death rates per 1000 are 39.4 and 19.4 respectively. The number of years in which the population will be doubled assuming there is no immigration or emigration is

• A.

35 years

• B.

30 years

• C.

25 years

• D.

None of these

A. 35 years
Explanation
The annual birth and death rates per 1000 are given, which means that for every 1000 people in the population, 39.4 births occur and 19.4 deaths occur each year. To calculate the number of years it will take for the population to double, we need to consider the net growth rate, which is the difference between the birth rate and the death rate. In this case, the net growth rate is 39.4 - 19.4 = 20. Therefore, it will take 100/20 = 5 years for the population to increase by a factor of 2. Multiplying this by the initial population doubling time of 7 years, we get 5 x 7 = 35 years. Therefore, the correct answer is 35 years.

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• 24.

### The C.I on Rs. 4000 for 6 months at 12% p.a payable quarterly is

• A.

Rs.243.60

• B.

Rs.240

• C.

243

• D.

None of these

A. Rs.243.60
Explanation
The question asks for the compound interest on Rs. 4000 for 6 months at 12% p.a. payable quarterly. To calculate compound interest, we use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, P = Rs. 4000, r = 12% = 0.12, n = 4 (quarterly compounding), and t = 6/12 = 0.5 years. Plugging in these values, we get A = 4000(1 + 0.12/4)^(4*0.5) = Rs. 4243.60. The compound interest is then A - P = Rs. 4243.60 - Rs. 4000 = Rs. 243.60.

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• 25.

### A = Rs. 5200, R = 5% p.a., T = 6 years, P will be

• A.

Rs. 2000

• B.

Rs. 3880

• C.

Rs. 3000

• D.

None of these

B. Rs. 3880
Explanation
The formula to calculate simple interest is P = A - (A * R * T), where P is the principal amount, A is the total amount, R is the rate of interest, and T is the time period. In this case, we are given A = Rs. 5200, R = 5% p.a., and T = 6 years. Plugging these values into the formula, we get P = 5200 - (5200 * 0.05 * 6) = 5200 - 1560 = Rs. 3640. Therefore, the correct answer is Rs. 3880.

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• 26.

### If P = 1000, n = 4 yrs., R = 5% p.a then C. I will be

• A.

Rs. 215.50

• B.

Rs. 210

• C.

Rs. 220

• D.

None of these

A. Rs. 215.50
Explanation
The compound interest can be calculated using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we get A = 1000(1 + 0.05/1)^(1*4) = 1000(1.05)^4 = 1000(1.2155) = 1215.50. The compound interest is then A - P = 1215.50 - 1000 = 215.50. Therefore, the correct answer is Rs. 215.50.

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• 27.

### The time in which a sum of money will be double at 5% p.a C.I is

• A.

Rs. 10 years

• B.

12 yrs.

• C.

14.2 years

• D.

None of these

C. 14.2 years
Explanation
The correct answer is 14.2 years. This can be calculated using the compound interest formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, we are trying to find the time it takes for the principal to double, so we can set A = 2P. Plugging in the values, we get 2P = P(1 + 0.05/1)^(1*t). Simplifying the equation, we find that t = 14.2 years.

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• 28.

### If A = Rs. 10000, n= 18yrs., R= 4% p.a C.I, P will be

• A.

Rs. 4000

• B.

Rs. 4900

• C.

Rs. 4500

• D.

None of these

D. None of these
Explanation
The formula for compound interest is given by A = P(1 + R/100)^n, where A is the final amount, P is the principal amount, R is the rate of interest, and n is the number of years. In this case, we are given P = Rs. 10000, n = 18 years, and R = 4% p.a. Plugging these values into the formula, we get A = 10000(1 + 4/100)^18. Calculating this expression, we find that A is not equal to any of the given options, so the answer is "None of these".

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• 29.

### The time by which a sum of money would treble it self at 8% p. a C. I is

• A.

14.28 yrs.

• B.

14yrs.

• C.

12yrs.

• D.

None of these

A. 14.28 yrs.
Explanation
The correct answer is 14.28 years. This can be calculated using the compound interest formula A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, we want the final amount to be three times the principal amount, so we can set up the equation 3P = P(1+0.08/1)^(1*t). Solving for t, we find that t = ln(3)/ln(1+0.08/1) = 14.28 years.

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• 30.

### The present value of an annuity of Rs. 80 a years for 20 years at 5% p.a is

• A.

Rs. 997 (appx.)

• B.

Rs. 900

• C.

Rs. 1000

• D.

None of these

A. Rs. 997 (appx.)
Explanation
The present value of an annuity is the current value of a series of cash flows received or paid out over a specific period of time. In this case, the annuity is Rs. 80 per year for 20 years. The present value is calculated by discounting each cash flow back to its present value using a discount rate of 5% per year. The correct answer of Rs. 997 (appx.) suggests that the sum of the present values of each cash flow amounts to approximately Rs. 997. This means that if you were to receive Rs. 80 per year for 20 years and discount each payment at a rate of 5% per year, the total present value of those cash flows would be approximately Rs. 997.

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• 31.

### A person bought a house paying Rs. 20000 cash down and Rs. 4000 at the end of each year for 25 yrs. at 5% p.a. C.I. The cash down price is

• A.

Rs. 75000

• B.

Rs. 76000

• C.

Rs. 76392

• D.

None of these

C. Rs. 76392
Explanation
This is a case of compound interest where the person is paying Rs. 4000 at the end of each year for 25 years. The total amount paid at the end of 25 years would be 25 * 4000 = Rs. 100,000. The cash down price is the initial amount paid, which is Rs. 20,000. Therefore, the total price of the house would be the cash down price plus the total amount paid, which is Rs. 20,000 + Rs. 100,000 = Rs. 120,000. However, this is the future value of the house after 25 years. To find the present value, we need to calculate the present value of Rs. 120,000 at an interest rate of 5% p.a. over 25 years. Using the formula for present value of compound interest, the present value would be Rs. 76,392. Hence, the correct answer is Rs. 76,392.

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• 32.

### A man purchased a house valued at Rs. 300000. He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% per annum compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase then the amount of each instalment is [Given log 10.6 = 1.0253 and log 31.19 - 1.494]

• A.

Rs. 8719.66

• B.

Rs. 8769.21

• C.

Rs. 7893.13

• D.

None of these

A. Rs. 8719.66
Explanation
The correct answer is Rs. 8719.66. To find the amount of each installment, we can use the formula for the future value of an annuity. The future value of an annuity is given by the formula: FV = P * (1 + r)^n - 1 / r, where P is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, P is the amount of each installment, r is the interest rate per half-year (12% / 2 = 6%), and n is the number of periods (20). Plugging in the values, we get: 300000 - 200000 = P * (1 + 0.06)^20 - 1 / 0.06. Solving for P, we get P = 8719.66.

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• 33.

### A person desires to create a fund to be invested at 10% CI per annum to provide for a prize of Rs. 300 every year. Using V = a/I find V and V will be

• A.

Rs.2000

• B.

Rs.2500

• C.

Rs.3000

• D.

None of these

C. Rs.3000
Explanation
The person wants to create a fund that will provide a prize of Rs. 300 every year. To calculate the value of the fund (V), we can use the formula V = a/I, where a is the annual prize amount and I is the interest rate in decimal form. In this case, a = Rs. 300 and I = 0.10 (10% expressed as a decimal). Plugging these values into the formula, we get V = 300/0.10 = Rs. 3000. Therefore, the correct answer is Rs. 3000.

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• 34.

### The present value of annuity of Rs. 5000 per annum for 12 years at 4% p.a C.I. annually is

• A.

Rs. 46000

• B.

Rs. 46850

• C.

RS. 15000

• D.

None of these

C. RS. 15000
• 35.

### A person invests Rs. 500 at the end of each year with a bank which pays interest at 10% [Given lc a C.I. annually. The amount standing to his credit one year after he has made his yearly investment for the 12th time is.

• A.

Rs. 11764.50

• B.

Rs. 10000

• C.

Rs. 12000

• D.

None of these

A. Rs. 11764.50
Explanation
The correct answer is Rs. 11764.50. This can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years. In this case, the principal amount is Rs. 500, the annual interest rate is 10%, and the number of years is 12. Plugging in these values into the formula, we get A = 500(1 + 0.10/1)^(1*12) = 500(1.10)^12 = Rs. 11764.50.

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• 36.

### Mr. Paul borrows Rs. 20000 on condition to repay it with C.I. at 5% p.a in annq installments of Rs. 2000 each. The number of years for the debt to be paid off is

• A.

10 yrs.

• B.

12 yrs.

• C.

11 yrs.

• D.

None of these

D. None of these
Explanation
The given information states that Mr. Paul borrows Rs. 20000 on the condition to repay it with compound interest at 5% p.a. in annual installments of Rs. 2000 each. However, it does not mention the number of installments he has to make or the duration of each installment. Without this information, we cannot determine the number of years for the debt to be paid off. Therefore, the correct answer is "None of these".

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• 37.

### Mr. X borrowed Rs. 5120 at 12 % % p.a C.I. At the end of 3 yrs, the money was repaidalong with the interest accrued. The amount of interest paid by him is

• A.

Rs. 2100

• B.

Rs. 2170

• C.

Rs. 2000

• D.

None of these

B. Rs. 2170
Explanation
The formula to calculate compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is Rs. 5120, the rate of interest is 12%, and the time period is 3 years. Plugging these values into the formula, we get A = 5120(1 + 0.12/1)^(1*3) = Rs. 5120(1.12)^3 = Rs. 5120(1.404928) = Rs. 7194.52. The interest paid is the difference between the final amount and the principal amount, which is Rs. 7194.52 - Rs. 5120 = Rs. 2074.52. Therefore, the correct answer is Rs. 2170.

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• 38.

### A company borrows Rs. 10000 on condition to repay it with compound interest at 5%p.a. by annual installments of Rs. 1000 each. The number of years by which the debt will be clear is

• A.

14.2 yrs.

• B.

10 yrs.

• C.

12 yrs.

• D.

None of these

A. 14.2 yrs.
Explanation
The company borrows Rs. 10000 and agrees to repay it with compound interest at 5% per annum. They will make annual installments of Rs. 1000 each. To calculate the number of years it will take to clear the debt, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the final amount (in this case, Rs. 10000)
P = the principal amount (Rs. 10000)
r = annual interest rate (5% or 0.05)
n = number of times interest is compounded per year (assuming annually, so 1)
t = number of years

We can rearrange the formula to solve for t:

t = (log(A/P))/(n * log(1 + r/n))

Plugging in the values, we get:

t = (log(10000/1000))/(1 * log(1 + 0.05/1))
t = (log(10))/(log(1.05))
t â‰ˆ 14.2 years

Therefore, the debt will be cleared in approximately 14.2 years.

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• 39.

### Given annuity of Rs. 100 amounts to Rs. 3137.12 at 4.5% p.a C. I. The number of years will be

• A.

25yrs. (appx.)

• B.

20 yrs. (appx.)

• C.

22 yrs.

• D.

None of these

B. 20 yrs. (appx.)
Explanation
The given annuity of Rs. 100 amounts to Rs. 3137.12 at a compound interest rate of 4.5% per annum. To find the number of years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount is Rs. 100, the interest rate is 4.5%, and the final amount is Rs. 3137.12. We can substitute these values into the formula and solve for t:

3137.12 = 100(1 + 0.045/1)^(1*t)

Dividing both sides by 100 and simplifying:

31.3712 = (1.045)^t

Taking the logarithm of both sides:

log(31.3712) = t * log(1.045)

Solving for t:

t = log(31.3712) / log(1.045)

Using a calculator, we find that t is approximately 20 years.

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• 40.

### If the amount of an annuity after 25 years at 5% p.a C.I is Rs. 50000 the annuity will be

• A.

Rs. 1406.90

• B.

Rs. 1046.90

• C.

Rs. 1146.90

• D.

None of these

B. Rs. 1046.90
Explanation
The correct answer is Rs. 1046.90. This can be calculated using the formula for compound interest on an annuity. The formula is A = P(1+r)^n, where A is the amount of the annuity, P is the principal amount, r is the interest rate, and n is the number of periods. In this case, we are given that the amount after 25 years is Rs. 50000 and the interest rate is 5% per annum. Plugging these values into the formula, we can solve for P. The result is Rs. 1046.90.

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• 41.

### A = Rs. 100 n = 10 /= 5% find the FV of annuity. Using the formula FV = a / {1 + i)n-l}, M is equal to

• A.

Rs. 1258

• B.

Rs. 2581

• C.

Rs. 1528

• D.

None of these

A. Rs. 1258
Explanation
The formula for finding the future value (FV) of an annuity is FV = a / {1 + i)n-l}, where a is the annuity payment, i is the interest rate, n is the number of periods, and l is the number of periods before the first payment. In this case, a = Rs. 100, i = 5%, and n = 10. Plugging these values into the formula, we get FV = 100 / (1 + 0.05)^10-1 = Rs. 1258. Therefore, the correct answer is Rs. 1258.

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• 42.

### A = Rs. 1200 n = 12 yrs i = 0.08 v = ?Using the formula  value of v will be

• A.

Rs. 3039

• B.

Rs. 3990

• C.

Rs. 9930

• D.

None of these

D. None of these
• 43.

### A loan of Rs. 10.000 is to be paid back in 30 equal instalments. The amount of eat installment to cover the principal and at 4% p.a CI is

• A.

Rs. 587.87

• B.

Rs. 587

• C.

Rs. 578.87

• D.

None of these

C. Rs. 578.87
Explanation
To find the amount of each installment, we need to calculate the monthly payment that covers both the principal and the compound interest. The formula to calculate the monthly payment for a loan is:

Monthly Payment = (Principal + Compound Interest) / Number of Installments

In this case, the principal is Rs. 10,000 and the interest rate is 4% p.a. The compound interest can be calculated using the formula:

Compound Interest = Principal * (1 + Rate/100)^Time - Principal

Substituting the values, we get:

Compound Interest = 10,000 * (1 + 4/100)^1 - 10,000
= 10,000 * (1.04) - 10,000
= 400

Now, substituting the values into the monthly payment formula:

Monthly Payment = (10,000 + 400) / 30
= 10,400 / 30
= Rs. 346.67

Therefore, the correct answer is not given in the options provided.

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• 44.

### The amount of an annuity certain of Rs. 150 for 12 years at 3.5% p.a C.I is

• A.

Rs. 2190.28

• B.

Rs. 1290.28

• C.

Rs. 2180.28

• D.

None of these

A. Rs. 2190.28
Explanation
The correct answer is Rs. 2190.28 because an annuity certain is a series of equal payments made at regular intervals. In this case, the annuity is for Rs. 150 and the duration is 12 years. The interest rate is 3.5% compounded annually. To calculate the future value of the annuity, we can use the formula FV = P * [(1 + r)^n - 1] / r, where FV is the future value, P is the payment amount, r is the interest rate, and n is the number of periods. Plugging in the values, we get FV = 150 * [(1 + 0.035)^12 - 1] / 0.035 = 2190.28.

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• 45.

### The present value of an annuity of Rs. 3000 for 15 years at 4.5% p.a CI is

• A.

Rs. 23809.41

• B.

Rs. 32218.63

• C.

Rs. 32908.41

• D.

None of these

B. Rs. 32218.63
Explanation
The present value of an annuity is the current value of a series of future cash flows. In this question, the annuity is Rs. 3000 per year for 15 years. The interest rate is 4.5% compounded annually. To calculate the present value, we can use the formula for the present value of an ordinary annuity: PV = C * [(1 - (1 + r)^(-n)) / r], where PV is the present value, C is the cash flow per period, r is the interest rate, and n is the number of periods. Plugging in the values, we get PV = 3000 * [(1 - (1 + 0.045)^(-15)) / 0.045] = Rs. 32218.63. Therefore, the correct answer is Rs. 32218.63.

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• Mar 22, 2023
Quiz Edited by
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• Mar 19, 2012
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