The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b $\mathrm { n } = \log _ { 1.025 } 2$ In how many years will the investment double, to the nearest tenth of a
Year?
A) 28.1 years
B) 3.5 years
C) 7.0 years
D) 14.0 years

Question

Quizplus · Accepted Answer

To find the number of years it takes for an investment to double with a 10% annual interest rate compounded quarterly, we use the formula for the number of periods $ n = \frac{\log(2)}{\log(1 + r)} $, where $ r $ is the quarterly interest rate. Given $ r = 0.10/4 = 0.025 $, the formula becomes $ n = \log_{1.025}(2) $. To convert the number of quarters to years, we divide by 4. The exact number of quarters is not given, but since the interest rate is 10% compounded quarterly, it typically takes fewer than 10 years to double. The correct answer, 7.0 years, is found by understanding that the investment doubles faster than linearly due to compounding, making 7.0 years a reasonable period for doubling at a 10% annual rate compounded quarterly.

The Number of Quarters Needed to Double an Investment When n=log⁡1.0252\mathrm { n } = \log _ { 1.025 } 2n=log1.025​2

The Number of Quarters Needed to Double an Investment When $\mathrm { n } = \log _ { 1.025 } 2$