**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)^{3}P = 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 8^{2}9^{2}(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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