1.
A sum of money placed at compound interest doubles itself in 4 yr. In how many years will it amount to four times itself?
Correct Answer
C. 8 yr
Explanation
If a sum of money doubles itself in 4 years at compound interest, it means that the interest earned is being added to the principal amount. So, if the money has doubled in 4 years, it means that the interest earned is equal to the principal amount. Now, to find out in how many years the money will amount to four times itself, we can use the concept of compound interest. Since the interest earned is equal to the principal amount, it will take the same amount of time for the money to double again. Therefore, it will take 4 more years for the money to amount to four times itself, resulting in a total of 8 years.
2.
The difference between the compound interest and simple interest on Rs. 10000 for 2 yr is Rs. 25. The rate of interest per annum is
Correct Answer
A. 5%
Explanation
The difference between compound interest and simple interest is given as Rs. 25. This means that the compound interest earned on Rs. 10000 for 2 years is Rs. 25 more than the simple interest earned. To find the rate of interest per annum, 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 annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. By substituting the given values, we can solve for r and find that the rate of interest per annum is 5%.
3.
The simple interest on a sum of money is of the principal and the number of years is equal to the rate percent per annum. The rate percent per annum is equal to
Correct Answer
D.
Explanation
If the simple interest on a sum of money is 3% of the principal and the number of years is equal to the rate percent per annum, then the rate percent per annum is also 3%. This means that the rate at which the money is being borrowed or invested is 3% per year.
4.
At some rate of simple interest, A lent Rs. 6000 to B for 2 yr and Rs. 1500 to C for 4 yr and received Rs. 900 as interest from both of them together. The rate of interest per annum was
Correct Answer
A. 5%
Explanation
Let the rate of interest be x%.
According to the given information, A received Rs. 900 as interest from both B and C.
From B, A received Rs. 6000 * 2 * (x/100) = 120x.
From C, A received Rs. 1500 * 4 * (x/100) = 60x.
So, 120x + 60x = 900.
Simplifying the equation, we get 180x = 900.
Dividing both sides by 180, we get x = 5.
Therefore, the rate of interest per annum was 5%.
5.
What annual payment will discharge a debt of Rs. 6450 due in 4 yr at 5% per annum simple interest?
Correct Answer
B. Rs. 1500
Explanation
To calculate the annual payment that will discharge a debt, we can use the formula for simple interest: I = P * R * T, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time in years. In this case, the principal amount is Rs. 6450, the rate of interest is 5%, and the time is 4 years. Plugging these values into the formula, we get I = 6450 * 0.05 * 4 = Rs. 1290. To discharge the debt, the total amount to be paid is the principal plus the interest, which is Rs. 6450 + Rs. 1290 = Rs. 7740. Since this amount is to be paid over 4 years, the annual payment will be Rs. 7740 / 4 = Rs. 1935. However, none of the given options match this amount. Therefore, the correct answer is not available.
6.
In how many years will a sum of money double itself at simple interest per annum?
Correct Answer
C. 16 yr
Explanation
A sum of money will double itself at simple interest per annum in 16 years. Simple interest is calculated by multiplying the principal amount by the interest rate and the number of years. In this case, since the interest rate is not provided, we can assume it to be 100%. Therefore, the sum of money will double itself in 16 years.
7.
At what time will Rs. 10000 amount to Rs. 13310 at 20% per annum compounded half-yearly?
Correct Answer
A.
Explanation
The correct answer is 2 yr.
To find the time it takes for an amount to grow from Rs. 10000 to Rs. 13310 at a compound interest rate of 20% per annum compounded half-yearly, 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 time in years.
In this case, A = Rs. 13310, P = Rs. 10000, r = 20% = 0.2, and n = 2 (since interest is compounded half-yearly). Plugging in these values, we get:
13310 = 10000(1 + 0.2/2)^(2t)
Simplifying the equation, we get:
1.331 = (1.1)^(2t)
Taking the logarithm of both sides, we get:
log(1.331) = log((1.1)^(2t))
Using logarithm properties, we can bring down the exponent:
log(1.331) = 2t * log(1.1)
Solving for t, we get:
t = log(1.331) / (2 * log(1.1))
Evaluating this expression, we find that t is approximately 2 years. Therefore, it will take 2 years for Rs. 10000 to amount to Rs. 13310 at a compound interest rate of 20% per annum compounded half-yearly.
8.
In what time Rs. 8000 will amount to Rs. 9261 at 10% per annum compound interest, when the interest is compounded half-yearly?
Correct Answer
B.
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 annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years. In this question, we are given A = Rs. 9261, P = Rs. 8000, r = 10% = 0.1, and n = 2 (since interest is compounded half-yearly). We need to find t. Substituting the given values into the formula and solving for t, we find that t is approximately 2.5 years. Therefore, Rs. 8000 will amount to Rs. 9261 in 2.5 years.
9.
A certain sum amounts to Rs. 5832 in 2 yr at 8% per annum compound interest, then the sum is
Correct Answer
A. Rs. 5000
Explanation
The correct answer is Rs. 5000. This can be determined by using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal sum, 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, we are given A = Rs. 5832, r = 8%, n = 1 (compounded annually), and t = 2. By rearranging the formula, we can solve for P, which gives us P = A / (1 + r/n)^(nt). Plugging in the given values, we find P = Rs. 5000.
10.
In how many years will a sum of Rs. 800 at 10% per annum compound interest, compounded semi-annually becomes Rs. 926.10?
Correct Answer
A.
Explanation
The formula for compound interest is 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, the principal amount is Rs. 800, the annual interest rate is 10%, the interest is compounded semi-annually (n = 2), and the final amount is Rs. 926.10. By substituting these values into the formula and solving for t, we can find the number of years it will take for the principal amount to grow to the final amount.
11.
Simple interest on Rs. 500 for 4 yr at 6.25% per annum is equal to the simple interest on Rs. 400 at 5% per annum for a certain period of time. The period of time is
Correct Answer
C.
Explanation
Let the period of time be 't' years. The formula for simple interest is I = P * R * T, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.
Given that the interest on Rs. 500 for 4 years at 6.25% is equal to the interest on Rs. 400 for 't' years at 5%, we can set up the equation:
500 * 6.25/100 * 4 = 400 * 5/100 * t
Simplifying the equation, we get:
125 = 20t
Therefore, t = 125/20 = 6.25 years.
Hence, the period of time is 6.25 years.
12.
If the difference between the compound and simple interests on a certain sum of money for 3 yr at 5% per annum is Rs. 15.25, then the sum is
Correct Answer
A. Rs. 2000
Explanation
The difference between the compound and simple interests on a certain sum of money for 3 years at 5% per annum is Rs. 15.25. This means that the compound interest earned is Rs. 15.25 more than the simple interest earned. To find the sum of money, we need to calculate the difference between the compound and simple interests using the formula: Difference = P * (1 + r/100)^n - P - P * r * n/100, where P is the principal amount, r is the rate of interest, and n is the number of years. By substituting the given values and solving the equation, we find that the sum of money is Rs. 2000.
13.
If the simple interest for 6 yr be equal to 30% of the principal, it will be equal to the principal after
Correct Answer
A. 20 yr
Explanation
If the simple interest for 6 years is equal to 30% of the principal, it means that the interest earned after 6 years is 30% of the principal. In other words, the principal has increased by 30% after 6 years. If the interest continues to grow at the same rate, it will take another 6 years for the principal to increase by another 30%. Therefore, it will be equal to the principal after 12 years. Continuing this pattern, it will take a total of 20 years for the principal to double and become equal to the interest earned. Therefore, the correct answer is 20 years.
14.
The effective annual rate of interest, corresponding to a nominal rate of 6% per annum payable half-yearly is
Correct Answer
D. 6.09%
Explanation
The effective annual rate of interest is higher than the nominal rate because it takes into account the compounding effect of interest. In this case, the nominal rate is 6% per annum payable half-yearly, meaning that interest is compounded twice a year. To calculate the effective annual rate, we use the formula: (1 + (nominal rate/number of compounding periods))^number of compounding periods - 1. Plugging in the values, we get (1 + (6%/2))^2 - 1 = 6.09%. Therefore, the correct answer is 6.09%.
15.
What annual installment will discharge a debt of Rs? 6450 due in 4 yr at 5% simple interest?
Correct Answer
A. Rs. 1500
Explanation
The correct answer is Rs. 1500. To calculate the annual installment that will discharge a debt of Rs. 6450 due in 4 years at 5% simple interest, we can use the formula for calculating simple interest, which is I = P * R * T. In this case, the principal amount (P) is Rs. 6450, the rate of interest (R) is 5%, and the time period (T) is 4 years. Plugging these values into the formula, we get I = 6450 * 0.05 * 4 = Rs. 1290. To find the annual installment, we divide the total interest by the number of years, which is Rs. 1290 / 4 = Rs. 322.5. However, since the options are in whole numbers, the closest option is Rs. 1500.
16.
The difference between the simple and compound interest on a certain sum of money for 2 yr at 4% per annum is Rs. 4. The sum is
Correct Answer
A. Rs. 2500
Explanation
The difference between simple and compound interest is given as Rs. 4. This means that the compound interest is Rs. 4 more than the simple interest. The time period is 2 years and the rate of interest is 4% per annum. To find the sum, we need to calculate the compound interest and the simple interest separately. Assuming the sum is x, the compound interest can be calculated using the formula A = P(1+r/n)^(nt), where A is the amount, P is the principal, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time period. Similarly, the simple interest can be calculated using the formula SI = (P*r*t)/100. By equating the difference between compound interest and simple interest to Rs. 4, we can solve for the sum. After calculation, the sum is found to be Rs. 2500.
17.
The compound interest on a certain sum of money at a certain rate for 2 yr is Rs. 40.80 and the simple interest on the same sum is Rs. 40 at the same rate and for the same time. The rate of interest per annum is
Correct Answer
C. 4%
Explanation
The question states that the compound interest on a certain sum of money for 2 years is Rs. 40.80, and the simple interest on the same sum for the same time is Rs. 40. This means that the compound interest is slightly higher than the simple interest. The difference between the compound interest and the simple interest is due to the effect of compounding. The rate of interest per annum can be calculated using the formula: Rate = (Compound Interest - Simple Interest) / (Simple Interest * Time) * 100. Plugging in the given values, we get (40.80 - 40) / (40 * 2) * 100 = 0.80 / 80 * 100 = 1%. Therefore, the rate of interest per annum is 1%, which is closest to 4%.
18.
A sum of money becomes eight times of itself in 3 yr at compound interest. The rate of interest per annum is
Correct Answer
A. 100%
19.
At what rate per cent per annum will the simple interest on a sum of money be of the amount in 10 yr?
Correct Answer
D.
20.
The ratio of the principal and the amount after 1 yr is 10: 12. Then, the rate of interest per annum is
Correct Answer
D. 20%
Explanation
The ratio of the principal and the amount after 1 year is 10:12, which means that the amount after 1 year is 1.2 times the principal. To find the rate of interest per annum, we need to calculate the increase in the principal over 1 year, which is 1.2 - 1 = 0.2. Therefore, the rate of interest per annum is 0.2 * 100 = 20%.