Question

David invests ₹ 25000 for 3 years at 6% per annum compound interest. Find

1. the interest for the first year.
2. the amount at the end of second year.
3. the compound interest for 3 years.

Answer 1

Given:

• Principal (P) = ₹ 25,000
• Rate of interest (r) = 6% per annum
• Time (n) = 3 years
• Interest is compounded annually

Step 1: Calculate the interest for the first year

Interest for the first year is simple interest on the principal, as compounding starts from the second year.

Interest for 1st year = `(P xx r xx 1)/100`

= `(25000 xx 6 xx 1)/100`

= ₹ 1500

Step 2: Calculate the amount at the end of second year

Amount after 1 year which becomes principal for next year:

A₁ = P + Interest for 1st year

A₁ = ₹ 25000 + ₹ 1500 

A₁ = ₹ 26500

Interest for the second year is calculated on ₹ 26500:

Interest for 2nd year = `(26500 xx 6 xx 1)/100`

Interest for 2nd year = ₹ 1590

Amount at the end of second year:

A₂ = A₁ + Interest for 2nd year

A₂ = ₹ 26500 + ₹ 1590

A₂ = ₹ 28090

Step 3: Calculate the compound interest for 3 years

Total amount at the end of 3 years using compound interest formula:

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

= `25000 xx (1 + 6/100)^3`

= 25000 × (1.06)³

Calculating (1.06)³:

1.06 × 1.06 = 1.1236;

1.1236 × 1.06 = 1.191016

So, A = 25000 × 1.191016 = ₹ 29775.40

Compound interest (C.I.):

C.I. = A – P

= 29775.40 – 25000

= ₹ 4775.40