Question

A borrowed a sum of Rs. 160000 from B at 10% per annum simple interest. At the same time he lent the same sum to C at the same rate on compound interest, compounded semi-annually for 2 years, Find the amount (in Rs.) earned by A in the whole transaction.
1. 4281
2. 4280
3. 2481
4. 2840

Answer 1

Correct Answer - Option 3 : 2481

 Given:

Principal = Rs. 160000

Rate = 10%

Time = 2 years

Formula used:

SI = (P × R × T)/100

Amount = P × (1 + r/100)^t

CI = Amount –  Principal

When compound semi-annually, r' = r/2 and t' = 2 × t

Calculation:

According to the question

SI = (160000 × 10 × 2)/100

⇒ Rs. 32000

Now,

Compounded amount when compounded semi annually = P(1 + r/200)^{2 × t}

Compounded amount = 160000[1 + 10/200)^{2 × 2}

⇒ 160000(21/20)⁴

⇒ Rs. (160000 × 21/20 × 21/20 × 21/20 × 21/20)

⇒ Rs. 194481

CI = Amount – Principal = (194481 – 160000)

⇒ Rs. 34481

Now, the amount earned by A in the whole transaction = CI – SI

⇒ (34481 – 32000)

⇒ Rs. 2481

∴ Required amount earned by A in the whole transaction is 2481