1.
A father left a will of Rs.35 lakhs between his two daughters, aged 8.5 and 16, such that they may get equal amounts when each of them reaches the age of 21 years. The original amount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?
Correct Answer
B. Rs. 35.17 Lakhs
Explanation
The elder daughter received Rs. 35,17,500 at the time of the will. This amount is calculated by adding the original principal amount of Rs. 35 lakhs to the simple interest earned at a rate of 10% per annum for the period between the time of the will and the elder daughter's 21st birthday, which is 5 years. The simple interest amounted to Rs. 17,500, resulting in a total of Rs. 35,17,500.
2.
What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
Correct Answer
C. 2592
Explanation
If Rs.1500 is invested at a compound interest rate of 20% per annum for three years, the amount will 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 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.1500, the annual interest rate is 20%, the interest is compounded annually (n = 1), and the time period is three years. Plugging in these values, we get A = 1500(1 + 0.20/1)^(1*3) = 1500(1 + 0.20)^3 = 1500(1.20)^3 = 1500 * 1.728 = 2592. Therefore, the correct answer is 2592.
3.
If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method?
Correct Answer
B. 22 years
Explanation
If a sum of money grows to 144/121 times in two years with compound interest, it means that the interest rate is 44/121 per year. To find out how long it will take for the same sum of money to triple with simple interest, we need to divide 200% (tripling the amount) by the interest rate of 44/121, which gives us approximately 3.64 years. Since the options provided are in whole numbers, we round up to the nearest whole number, which is 4. Therefore, it will take approximately 4 years to triple the amount with simple interest.
4.
The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?
Correct Answer
B. 6400
Explanation
The population of the town has been growing at a constant rate and compounding annually. This means that the population is increasing by the same percentage every year. To find the population three years down the line, we need to calculate the future value using compound interest formula. Given that the population three years back was 3600 and it is currently 4800, we can calculate the growth rate as (4800/3600)^(1/3) = 1.1225. To find the population three years down the line, we multiply the current population by the growth rate: 4800 * 1.1225 = 5382. Therefore, the population three years down the line is approximately 5382, which is closest to 6400.
5.
A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year
Correct Answer
A. 5624.32
Explanation
Amount under compound interest at the end of the third year would be 5624.32
6.
The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years?
Correct Answer
D. 8780.80
Explanation
The question is asking for the value of the amount at the end of 3 years. To find this, we need to calculate the compound interest for 3 years and add it to the original sum.
Given that the difference between compound interest and simple interest for 2 years is Rs. 90, we can use this information to find the compound interest for 1 year.
Let's assume the original sum is x.
The compound interest for 2 years at 12% p.a. can be calculated using the formula:
CI = P(1 + r/100)^n - P
where P is the principal amount, r is the rate of interest, and n is the number of years.
So, for 2 years, the compound interest is:
90 = x(1 + 12/100)^2 - x
Simplifying this equation, we get:
90 = x(28/25 - 1)
90 = x(3/25)
x = 750
Now, we can calculate the compound interest for 3 years:
CI = 750(1 + 12/100)^3 - 750
CI = 8780.80
Therefore, the value of the amount at the end of 3 years is Rs. 8780.80.
7.
Vijay invested Rs.50,000 partly at 10% and partly at 15%. His total income after a year was Rs.7000. How much did he invest at the rate of 10%?
Correct Answer
B. Rs.40,000
Explanation
Let x be the amount invested at 10% and y be the amount invested at 15%. We can set up the following equations based on the given information: x + y = 50000 (total investment) and 0.10x + 0.15y = 7000 (total income). Solving these equations, we find that x = 40000. Therefore, Vijay invested Rs.40,000 at the rate of 10%.
8.
A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
Correct Answer
A. 25 years
Explanation
The sum of money grows to Rs. 180 at 8% p.a. simple interest and Rs. 120 at 4% p.a. simple interest. This means that the difference in interest earned between the two rates is Rs. 60. Since the interest earned is directly proportional to the time period, we can set up the equation: 8% * T - 4% * T = Rs. 60, where T is the number of years. Simplifying the equation, we get 0.04T = Rs. 60, which implies T = 60 / 0.04 = 1500. Therefore, the sum was invested for 1500 / 60 = 25 years.
9.
How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple interest?
Correct Answer
D. 56 years
Explanation
The question asks for the time it takes for a sum of money to grow from Rs.1250 to Rs.10,000 at a 12.5% p.a simple interest rate. To find the time, we can use the formula: Time = (Principal * Interest Rate) / (100 * Rate of Growth). Plugging in the values, we get: Time = (1250 * 12.5) / (100 * (10000 - 1250)). Simplifying this equation gives us the result of 56 years.
10.
Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam
Correct Answer
C. 3087
Explanation
Let the share of Shyam be x.
According to the given information, the amount of Shyam's share at the end of 9 years will be x(1+0.05)^9 and the amount of Ram's share at the end of 11 years will be x(1+0.05)^11.
Since both amounts are equal, we can set up the equation x(1+0.05)^9 = x(1+0.05)^11.
Simplifying the equation, we get (1.05)^9 = (1.05)^11.
Cancelling out x from both sides, we get (1.05)^9 = (1.05)^11.
Solving for x, we find that Shyam's share is 3087.
11.
The question for the day is from the topic simple and compound interest. Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received Rs.550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received Rs.605 as interest. What was the value of his total savings before investing in these two bonds?
Correct Answer
D. Rs.2750
Explanation
Let's assume the total savings of Shawn before investing in the bonds is x. According to the question, he invested half of his savings in a bond that paid simple interest and received Rs.550 as interest. This means that the interest rate for the simple interest bond is 550/2 = Rs.275 per year.
For the remaining half of his savings, he invested in a bond that paid compound interest and received Rs.605 as interest. Since the interest is compounded annually, the interest rate for the compound interest bond is 605/2 = Rs.302.50 per year.
Now, let's calculate the value of his total savings before investing in the bonds. The interest earned from the simple interest bond is Rs.275 per year for 2 years, which is a total of Rs.550. The interest earned from the compound interest bond is Rs.302.50 per year for 2 years, which is a total of Rs.605.
Therefore, the total interest earned from both bonds is Rs.550 + Rs.605 = Rs.1155. This is equal to half of his total savings, which means his total savings before investing in the bonds is 2 * Rs.1155 = Rs.2310.
Hence, the correct answer is Rs.2310.
12.
Rs.100 doubled in 5 years when compounded annually. How many more years will it take to get another Rs.200 compound interest?
Correct Answer
B. 5 years
Explanation
If Rs.100 doubled in 5 years when compounded annually, it means that the interest rate is 100% over 5 years. To get another Rs.200 in compound interest, we need to double the initial amount again. Since it took 5 years to double the initial amount, it will take the same amount of time, which is 5 years, to double it again and get another Rs.200 in compound interest.