Question

Manoj invested a certain sum in a scheme for 2 years, which gives interest at the rate of 15% compounded annually. If the interest had been compounded 8 months, he would have gained Rs. 68 more, then what is the sum invested by Manoj?

1. Rs 8000
2. Rs 6500
3. Rs 6000
4. Rs 7000

Answer 1

Correct Answer - Option 1 : Rs 8000

Given:

Rate = 15%

Time = 2 years

Formula used:

For CI,

Amount = P(1 + r/100)n

Amount = P + CI

Here n is the time

Calculation:

Let the sum be x

Case1- When compounded in 8 months

2 years = 24 months

Number of times to pay the interest is 24/8 = 3 times

Rate for 2 years = 2 × 15 = 30%

Rate when compounded in 8 months = 30/3% = 10%

Amount = P(1 + r/100)n

⇒ x(1 + 10/100)3

⇒ 1331x/1000

Case2- When compounded annually

Amount = P(1 + r/100)n

⇒ x(1 + 15/100)2

⇒ 529x/400

Now, A/Q

1331x/1000 – 529x/400 = 68

⇒ 17x/2000 = 68

⇒ x = 8000

∴ The sum invested by Manoj is Rs 8000