Question

A sum of money becomes 4 times its present amount in 10 years when compounded annually. After how many years, will the sum become 16 times its initial value?
1. 15
2. 10
3. 20
4. 5
5. 25

Answer 1

Correct Answer - Option 3 : 20

Given:

Time taken for the sum of money to become 4 times its present value = 10 years

Formula Used:

When interest is compounded annually, the amount received is obtained as:

Amount = P × [1 + (R/100)]ⁿ

where P = Principal,

R = Rate of interest for compounding principal annually,

n = time period (in years)

Calculation:

∵ The sum becomes 4 times its initial value after 10 years,

We get the equation for amount as follows:

4P = P × [1 + (R/100)]¹⁰

⇒ 4 = [1 + (R/100)]¹⁰      ----(i)

Let's assume that the time taken by the sum to become 16 times its value = x years

Now, we get the equation for amount as follows:

16P = P × [1 + (R/100)]^x

⇒ 16 = [1 + (R/100)]^x

⇒ 4² = [1 + (R/100)]^x      ----(ii)

From equation (i), we get:

⇒ 42 = {[1 + (R/100)]¹⁰}²      ----(iii)

On combining eqautions (ii) and (iii), we get:

[1 + (R/100)]x = {[1 + (R/100)]10}2

⇒ x = 10 × 2 

⇒ x = 20

∴ The sum will become 16 times its initial amount after a period of 20 years.