Question

The present worth of the sum of Rs. 5,830, due 9 months hence, is Rs. 5,500. Find the rate of interest.

Answer 1

Given:

• Sum due (Future Value, A) = Rs. 5,830
• Present Worth (Principal, P) = Rs. 5,500
• Time = 9 months = `9/12 = 3/4` year

We have to find the Rate of Interest (R%) per annum, assuming simple interest.

Formula:

`A = P + (P xx R xx T)/100`

Substitute values:

`5830 = 5500 + (5500 xx R xx 3/4)/100`

Step 1: Subtract 5500 from both sides

`5830 - 5500 = (5500 xx R xx 3/4)/100`

`330 = (5500 xx R xx 3)/400`

Step 2: Simplify

`330 = (16500R)/400`

Multiply both sides by 400:

330 × 400 = 16500R

132000 = 16500R

Step 3: Solve for R

`R = 132000/16500`

R = 8

Rate of Interest = 8% per annum