Question

A man invests ₹ 50000 for 18 months at a certain rate of interest compounded half-yearly. At the end of 6 months, it amounts to ₹ 53000. Find

1. the rate of interest per annum. 
2. the amount after 18 months.

Answer 1

Given:

• Principal (P) = ₹ 50000
• Time = 18 months = 1.5 years
• Amount at the end of 6 months = ₹ 53000
• Interest compounded half-yearly

i. Find the rate of interest per annum.

Since interest is compounded half-yearly, the compounding period is 6 months.

Let the rate of interest per annum be r%, then the half-yearly interest rate = `r/2`.

Amount after 6 months = `P xx (1 + (r//2)/100) = 53000`

Substitute P = 50000:

`50000 xx (1 + r/200) = 53000`

Divide both sides by 50000:

`1 + r/200 = 53000/50000 = 1.06`

Therefore, `r/200 = 0.06`

⇒ r = 0.06 × 200

⇒ r = 12%

Rate of interest per annum = 12%.

ii. Find the amount after 18 months.

18 months = 3 half-yearly periods.

Using the compound interest formula for (n) periods:

`A = P xx (1 + r/200)^n`

A = 50000 × (1.06)³ 

Calculate:

1.06³ = 1.06 × 1.06 × 1.06

1.06³ = 1.191016

A = 50000 × 1.191016

A = ₹ 59550.8