Question

An amount is said to double in 5 years with compound interest. How many years will it take for the amount to grow to 8 times its original value?

• A. 15
• B. 16
• C. 17
• D. 18

Answer 1

Answer:

A. 15

If an amount doubles in 5 years, then:

$(1+r)^5 = 2$

We need the time when it becomes 8 times:

$(1+r)^t = 8$

Since $(8 = 2^3)$, rewrite:

$(1+r)^t = ( (1+r)^5 )^3$

So:
$(1+r)^t = (1+r)^{15}$

Equating powers:
$t = 15$

Final Answer:

$\boxed{15 \text{ years}}$