Question

In how many years will ₹ 8500 amount to ₹ 11313.50 at 10% per annum compound interest?

Answer 1

Given:

• Principal (P = ₹ 8500)
• Amount (A = ₹ 11313.50)
• Rate of interest (r = 10%) per annum (compound interest)
• Time (n = ?) number of years to find

Step-wise calculation:

1. The compound interest formula is:

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

2. Substitute the given values:

`11313.50 = 8500(1 + 10/100)^n`

11313.50 = 8500 × (1.1)ⁿ

3. Divide both sides by 8500:

`11313.50/8500 = (1.1)^n`

1.33 = (1.1)ⁿ

4. Take logarithm on both sides:

log (1.33) = n log (1.1)

5. Calculate values of logarithms using common logarithm base 10: 

log (1.33) ≈ 0.12385

log (1.1) ≈ 0.04139

6. Calculate (n):

`n = 0.12385/0.04139 ≈ 3`

The sum of ₹ 8500 will amount to ₹ 11313.50 in 3 years at 10% per annum compound interest.