The number of periods needed to double an investment when a lump sum is invested at 10%, compounded semiannually, is given by n $\mathrm { n } = \log _ { 1.05 } 2$ Find the number of years before the investment doubles in value, to the
Nearest tenth of a year.
A) 7.1 years
B) 28.4 years
C) 14.2 years
D) 3.6 years

Question

Quizplus · Accepted Answer

The formula to find the number of periods needed to double an investment with compound interest is $n = \frac{\log(2)}{\log(1 + r)}$, where $r$ is the interest rate per period. Since the interest is compounded semiannually at 10%, the rate per period is 5% or 0.05. Thus, $n = \frac{\log(2)}{\log(1.05)}$. This formula calculates the number of periods, not years. Since the compounding is semiannual, the number of years is half the number of periods. Calculating this gives approximately 14.2 periods, which when divided by 2 gives 7.1 years.

The Number of Periods Needed to Double an Investment When n=log⁡1.052\mathrm { n } = \log _ { 1.05 } 2n=log1.05​2

The Number of Periods Needed to Double an Investment When $\mathrm { n } = \log _ { 1.05 } 2$