Question

A man invests ₹ 12500 at 12% per annum compound interest for 3 years. Find

1. the interest for the first year.
2. the interest for third year.
3. the compound interest for 3 years.

Answer 1

Given:

• Principal (P) = ₹ 12500
• Rate of interest (r) = 12% per annum
• Time (n) = 3 years
• Compound interest compounded annually

Step-wise calculation:

Step 1: Interest for the first year

Simple interest for the first year same as compound interest for first year because it is on principal only.

Interest₁ = `(P xx r xx 1)/100`

= `(12500 xx 12 xx 1)/100`

= ₹ 1500

Step 2: Interest for the third year

Calculate the amount at the end of 2 years:

`A_2 = P(1 + r/100)^2`

= `12500 xx (1 + 12/100)^2`

= 12500 × (1.12)²

= 12500 × 1.2544

= ₹ 15680

Calculate the amount at the end of 3 years:

`A_3 = P(1 + r/100)^3`

= 12500 × (1.12)³

= 12500 × 1.404928

= ₹ 17561.60

Interest for the third year is amount difference between year 3 and year 2:

Interest₃ = A₃ – A₂

= 17561.60 – 15680

= ₹ 1881.60

Step 3: Compound Interest for 3 years

C.I. = A₃ – P

= 17561.60 – 12500

= ₹ 5061.60