Question

The simple interest on a sum of money for 3 years at 10% per annum is ₹ 1200. Find

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

Answer 1

Given:

• Simple Interest (S.I.) for 3 years = ₹ 1200
• Rate of Interest (R) = 10% per annum
• Time (T) = 3 years

i. Find the sum of money (Principal, P).

Step 1: Use the simple interest formula

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

Step 2: Substitute the known values and solve for P

`1200 = (P xx 10 xx 3)/100`

`1200 = (30P)/100`

1200 = 0.3P

`P = 1200/0.3`

P = 4000

The sum of money is ₹ 4000.

ii. Find the compound interest (C.I.) on this sum for one year payable half-yearly at the same rate 10% per annum.

Step 1: Understand the compounding frequency

Annual interest rate = 10%

Compounded half-yearly means the rate for each half year = `10/2` = 5%

Number of half-year periods in 1 year = 2

Step 2: Calculate amount (A) after one year using compound interest formula

`A = P xx (1 + R/(100 xx n))^(n xx T)` Where:

• P = 4000
• R = 10%
• n = 2 compounding periods per year
• T = 1 year

`A = 4000 xx (1 + 10/(100 xx 2))^(2 xx 1)`

A = 4000 × (1 + 0.05)²

A = 4000 × 1.1025

A = 4410

Step 3: Calculate compound interest

C.I. = A – P 

C.I. = 4410 – 4000 

C.I. = 410

The compound interest on this sum for one year payable half-yearly at 10% is ₹ 410.