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
(1331/1000)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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