Question

On a sum of money, the difference between CI for a year payable half yearly and the SI for a year is ₹ 80. If the rate of interest is 5%, find the sum.

Answer 1

Given:

• Difference between Cl for 1 year (half-yearly) and SI for 1 year = ₹ 80 
• Rate of interest r = 5% p.a.
• We need to find the principal P.

Step 1: Formulas

1. Simple Interest (SI) for 1 year:

`SI = P xx r/100`

2. Compound Interest (CI) for 1 year, half-yearly:

• Rate per half-year = `r/2` = 2.5%
• Number of half-year periods = 2

`A = P(1 + (r//2)/100)^2`

`CI = A - P = P(1 + 2.5/100)^2 - P`

`CI = P(1.025^2 - 1)`

`CI = P(1.050625 - 1)`

`CI = P * 0.050625`

Step 2: Difference between CI and SI

Difference = CI – SI

= P(0.050625 – 0.05)

= P · 0.000625

We are given that this difference = ₹ 80:

P · 0.000625 = 80

Step 3: Solve for P

`P = 80/0.000625`

P = 1,28,000