The number of periods needed to double an investment when a lump sum is invested at 2%, compounded semiannually, is given by n $\mathrm { n } = \log _ { 1.01 } 2$ 2. Use the change of base formula to find n, rounded to the nearest tenth.
A) 72.7 periods
B) 69.7 periods
C) 74.7 periods
D) 65.7 periods

Question

Quizplus · Accepted Answer

The change of base formula allows us to convert the logarithm to a more calculable form, specifically $\log_{1.01}2 = \frac{\log 2}{\log 1.01}$, where $\log$ represents the common logarithm (base 10). Using a calculator, we find $\frac{\log 2}{\log 1.01} \approx 69.7$. Therefore, it takes approximately 69.7 periods to double the investment.

The Number of Periods Needed to Double an Investment When n=log⁡1.012\mathrm { n } = \log _ { 1.01 } 2n=log1.01​2

The Number of Periods Needed to Double an Investment When $\mathrm { n } = \log _ { 1.01 } 2$