A sum of money becomes 4 times its present amount in 10 years when com

1.	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. 152. 103. 204. 55. 25
Answer» 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.

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. 152. 103. 204. 55. 25

Answer» 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.