# It will Amount to Eight Times Itself at the Same Rate of Interest in :

A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in

- 12 years
- 15 years
- 20 years
- 10 years

**Answer is (2): 15 years**

**Explanation:-**Let the principal be Rs.1 which become after Rs.2 after 5 years

Then 2 = 1(1 + R/100)

^{5}………………………… (1)

Let the principal of Rs.1 becomes Rs.8 after n years

Then, 8 = 1(1 + R/100)^{n} ……………………… (2)

(2)^{3} = 1 (1 + R/100)^{n}

Comparing equation (1) & (2)

Then, [1(1 + R/100)^{5}]^{3} = 1 (1 + R/100)^{n}

1 (1 + R/100)^{15} = 1 (1 + R/100)^{n}

n = 15

Then, the amount to eight times itself at the same rate of interest in 15 years.

Hence, the answer is (2) 15 years.