The number of quarters needed to double an investment when a lump sum is invested at 4%, compounded quarterly, is given b $\mathrm { n } = \frac { \ln 2 } { \ln 1.01 }$ . In how many years will the investment double, to the nearest tenth of a year?
A) 17.4 yr
B) 8.7 yr
C) 34.8 yr
D) 69.7 yr

Question

Quizplus · Accepted Answer

The formula given calculates the number of quarters needed to double an investment with quarterly compounding interest. To find the number of years, we divide the number of quarters by 4. First, calculate the value of $n$:$$n = \frac{\ln(2)}{\ln(1.01)} \approx 69.66$$This is the number of quarters. To convert to years:$$69.66 \div 4 \approx 17.4 \text{ years}$$Therefore, it takes approximately 17.4 years to double the investment.

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