Question

A certain sum amounts to Rs.23,927.68 at 12% p.a. in \(3{{3} \over 4}\) years, interest compounded yearly. The sum is:
1. Rs.15006.25
2. Rs.10056.25
3. Rs.15600.25
4. Rs.15625

Answer 1

Correct Answer - Option 4 : Rs.15625

Given:

Amount (A) = Rs.23,927.68

Rate (R) = 12%

Time (n) = \(3{{3} \over 4}\) years

Formula used:

A = P(1 + R/100)n

Where A → amount

P → principal

R → rate 

n → time

Calculations:

Amount after 3 years = P(1 + 12/100)³

⇒ P × (28/25) × (28/25) × (28/25)

Now rate for 3/4 years = 12 × 3/4 = 9%

So,the amount after 3 and (3/4) years, A = P × (28/25) × (28/25) × (28/25) × (109/100)

⇒ (A/P) = (2392768/1562500)

Since A = Rs.23,927.68

Thus P = 23927.68 × (1562500/2392768) = Rs.15625

∴ The sum is Rs.15625.