Question

In how many years will ₹ 18000 amount to ₹ 23805 at 15% per annum compound interest?

Answer 1

Given:

• Principal (P = ₹ 18000)
• Rate of interest per annum (r = 15%)
• Amount (A = ₹ 23805)
• Time = (n) years to be found

Step-wise calculation:

Using compound interest formula:

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

Substitute the given values:

`23805 = 18000(1 + 15/100)^n`

23805 = 18000 × (1.15)ⁿ

Divide both sides by 18000:

`23805/18000 = (1.15)^n`

1.3225 = (1.15)ⁿ

Take natural logarithm (ln) on both sides:

ln 1.3225 = n ln 1.15

Calculate the logarithms:

0.2793 = n × 0.1398

Solve for n:

`n = 0.2793/0.1398`

n = 2

The principal ₹ 18000 will amount to ₹ 23805 at 15% per annum compound interest in 2 years.