Question

Ruhi invests ₹ 12800 for 3 years at the rate of 10% per annum compound interest. Find

1. the sum due at the end of first year.
2. the interest for the second year.
3. the compound interest after 3 years.

Answer 1

Given:

• Principal (P) = ₹ 12,800
• Rate of interest (R) = 10% per annum
• Time (T) = 3 years
• Compound interest

Step-wise calculation:

i. Sum due at the end of first year

The compound interest formula for amount is:

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

For first year T = 1,

`A_1 = 12800 xx (1 + 10/100)^1`

A₁ = 12800 × 1.10

A₁ = ₹ 14080

ii. Interest for the second year

Amount at end of first year = ₹ 14,080

For second year T = 1,

Interest for second year = `A_1 xx R/100`

= `14080 xx 10/100`

= ₹ 1408

iii. Compound interest after 3 years

Calculate total amount after 3 years:

`A_3 = 12800 xx (1 + 10/100)^3`

A₃ = 12800 × 1.10³

A₃ = 12800 × 1.331

A₃ = ₹ 17036.8

Compound interest is the difference between total amount and principal:

C.I. = A₃ – P

= 17036.8 – 12800

= ₹ 4236.8