Compound Interest | Set-2

Question 1: If the compound interest on a certain sum for 2 years at 5% per annum is Rs 410, the simple interest at the same rate of interest for two years would be: 
Solution: Time = 2 years Rate =5% 
Compound Interest for 2 years= R + R + RxR/100
= 5 + 5 + 5×5/100 
= 10.25% 
Simple interest for 2 years = 2 x 5 =10% 
Hence, required SI = (410/10.25) x 10 
= 400

Question 2: If the amount is 1.331 times of the sum after 3 years at compound interest, the rate of interest per annum is 
Solution: Let the principal = P 
Amount after 3 years = 1.331P 
Let rate = R% 
Now use formula 
1.331P = P (1 + R/100)³
(11/10)³P = P(1 + R/100)³
11/10 = 1 + R/100 
1/10 = R/100 
R =10%

Question 3: The compound interest on Rs. 5000 in 2 years at 6% per annum, the interest being compounded half-yearly is: 
Solution: When the interest is compounded half-yearly 
1) Time doubles = 2 x 2 = 4 years 
2) Rate half = 6/2 = 3% 
Use formula 
Amount = 5000 x (1 + 3/100)⁴
= 5000 x 103/100 x 103/100 x 103/100 x 103/100 
= 5627.544 
Compound Interest = 5627.544 – 5000 
= 627.544

Question 4: A sum of money invested at compound interest amounts in 3 years to Rs. 2600 and in 4 years to Rs 2730.Find the interest rate per annum. 
Solution: Change in amount in 1 year = 2730 – 2600 = 130 
Required Rate % = (130 / 2600 ) x 100 
= 5 %

Question 5: At what rate per annum will Rs 8000 yield a compound interest of Rs. 1261 in 9 months interest being compounded quarterly? 
Solution: Let the Rate = 4 R% 
Principal = 8000 
CI = 9261 
Amount = 8000 + 1261 = 9261 
Interest is being compounded quarterly 
So, Time = 9 x (4 /12) = 3 
Rate = 4 R%/4 =R% 
Acc . to question 

           Principal           Amount
3rd year     8000       :       9261
1st year    ∛8000    :         ∛9261 
              20         :       21
                      +1

Rate (R%) = 1/20 x 100 = 5 % 
Required Rate = 4 x 5 = 20%

Question 6: A money lender borrows money at 5% per annum and pays the interest at the end of the year. He lends it at 8% per annum compound interest compounded half-yearly and receives the interest at the end of the year. In this way, he gains Rs 120.08 a year. The amount of money he borrows. 
Solution: 
Case (1)Rate = 5 % 
time = 1 year 
Case (2) When interest is compounded half yearly 
Rate = 8/2 =4% 
Time = 1 x 2 = 2 years 
Effective rate % for 2 years = 4 + 4 + 4×4/100 = 8.16 % 
Difference in rates= 8.16% – 5 = 3.16 % 
Given that he gains 120.08. So, 
3.16 -> 120.08 
1 -> 38 
100 -> 3800 
Hence, the amount of money he borrows Rs 3800

Question 7: Ram buy a second hand bike of Rs 13600 as a loan which along with interest is to be paid in two equal annual installment.If the rate of interest is 12.5 % compounded annually, then the value of each installment is: 
Solution: Rate of interest = 12.5% =1/8 

                 Principal        Installment
1st year          8                 9                (1)
2nd year          82                92                (2)

Since, installment is equal in both years so multiply (1) by 9 
Total principal = 64 + 72 = 136 
136 -> 13600 
1 -> 100 
81 -> 8100 
So, each installment equal to Rs 8100.

Question 8: A farmer borrowed some money from a bank at 8% simple interest per annum. He lended this money to another person at 10% compound interest per annum, and made a profit of Rs 30000 in 2 years. The farmer borrowed the amount is 
Solution: Let the farmer borrowed = Rs x 
Simple Interest in 2 years = (x * 8 * 2)/ 100 
Compound Interest in 2 years = x(1 + 10/100)²
Acc. to question 
x(1 + 10/100)² – x + (x * 8 * 2)/ 100 = 30000 
121x/100 – 116x/100 = 30000 
5x/100 = 30000 
x = 600000 
Hence, the farmer borrowed Rs 600000.

Question 9: A man borrowed some money and agreed to pay-off by paying Rs 1331 at the end of the 1st year and Rs 2420 at the end of the 2nd year. If the rate of compound interest is 10% per annum, then the sum is 
Solution: 10% = 1/10 
He pays some amount along with 10% interest in 1st year 

1st year     10       11
2nd year     100      121

After 1st year he returns 1331 
So, 11 -> 1331 
1 -> 121 
10 -> 1210 
After 2nd year he returns 2420 
So, 121 -> 2420 
1 -> 20 
100 -> 2000 
Hence total sum = 1210 + 2000 = Rs 3210

Question 10: A sum of money is invested at 10% compound interest . It would fetch Rs 120 more if interest is compounded half-yearly. The sum is 
Solution: Let principal = 400 
Rate = 10 % 
So, first year CI = (400 * 10)/ 100 = 40 

If compounded half-yearly then 
Rate = 10%/2 = 5% 
Time = 2 x 1 = 2 year 
Interest Rate in 2 year = 5 + 5 + 5×5/100 
= 10.25% 
CI in 2 year = (400 x 10.25) / 100 
= 41 
Acc. to ques if compounded half yearly it fetches Rs 120 more. 
41 – 40 = 120 
1 = 120 
400 = 48000 
Hence, the sum of money= Rs 48000

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