The number of periods needed to double an investment when a lump sum is invested at 11%, compounded semiannually, is given by n $\mathrm { n } = \frac { \ln 2 } { \ln 1.055 }$ . Find n, rounded to the nearest tenth.
A) 12.9 periods
B) 15.9 periods
C) 17.9 periods
D) 8.9 periods

Question

Quizplus · Accepted Answer

The formula to find the number of periods needed to double an investment with compound interest is $ n = \frac{\ln(2)}{\ln(1 + r)} $, where $ r $ is the interest rate per period. Since the interest rate is 11% per annum compounded semiannually, the rate per period is $ \frac{11\%}{2} = 5.5\% = 0.055 $. Substituting $ r = 0.055 $ into the formula gives $ n = \frac{\ln(2)}{\ln(1.055)} $, which when calculated and rounded to the nearest tenth, gives approximately 12.9 periods.

The Number of Periods Needed to Double an Investment When n=ln⁡2ln⁡1.055\mathrm { n } = \frac { \ln 2 } { \ln 1.055 }n=ln1.055ln2​

The Number of Periods Needed to Double an Investment When $\mathrm { n } = \frac { \ln 2 } { \ln 1.055 }$