The number of periods needed to double an investment when a lump sum is invested at 2%, compounded semiannually, is given by n $\mathrm { n } = \frac { \ln 2 } { \ln 1.01 }$ . Find the number of years before the investment doubles in value, to the
Nearest tenth of a year.
A) 34.8 yr
B) 139.3 yr
C) 17.4 yr
D) 69.7 yr

Question

Quizplus · Accepted Answer

The formula given calculates the number of compounding periods required to double an investment. Since the interest is compounded semiannually, each period is half a year. Plugging the values into the formula gives $ n = \frac{\ln(2)}{\ln(1.01)} \approx 69.7 $ periods. To find the number of years, divide by 2 (since there are 2 periods in a year), which gives approximately 34.8 years.

The Number of Periods Needed to Double an Investment When n=ln⁡2ln⁡1.01\mathrm { n } = \frac { \ln 2 } { \ln 1.01 }n=ln1.01ln2​

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