Question

The simple interest on a sum of money for 3 years at 4% per annum is ₹ 510. Find:

1. the sum of money. 
2. the C.I. on this sum for one year payable half-yearly at the same rate.

Answer 1

Given:

• Simple Interest (S.I.) for 3 years = ₹ 510
• Rate of interest per annum (R) = 4 %

We need to find:

1. The sum of money (Principal, P).
2. The Compound Interest (C.I.) on this sum for one year, payable half-yearly at the same rate.

Step-wise calculation:

Step 1: Calculate the Principal using Simple Interest formula

Simple Interest formula:

`S.I. = (P xx R xx T)/100`

Plug in the known values:

`510 = (P xx 4 xx 3)/100`

Simplify:

`510 = (12P)/100`

Multiply both sides by 100:

510 × 100 = 12P

51000 = 12P

Divide both sides by 12:

`P = 51000/12`

P = 4250

So, the sum of money is ₹ 4250.

Step 2: Calculate Compound Interest for 1 year, compounded half-yearly

• Principal (P = 4250)
• Annual rate (R = 4%)
• Time (T = 1) year
• Compounded half-yearly, so number of compounding periods, (n = 2)
• Rate per half year = `(4/2 = 2%)`

Compound amount formula:

`A = P xx (1 + R/(100 xx n))^(nt)`

= `4250 xx (1 + 4/(2 xx 100))^(2 xx 1)`

= 4250 × (1 + 0.02)²

= 4250 × (1.02)²

Calculate:

(1.02)² = 1.0404

So, A = 4250 × 1.0404 = 4421.70

Compound Interest (C.I.)

= A – P

= 4421.70 – 4250 

= 171.70