The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b $n = \log 1.025^2$ 2. Use the change of base formula to find n, rounded to the nearest tenth.
A) 33.1 quarters
B) 28.1 quarters
C) 31.1 quarters
D) 24.1 quarters

Question

Quizplus · Accepted Answer

To double an investment with a 10% annual interest rate compounded quarterly, the interest rate per quarter is 2.5% or 0.025. The formula given is $n = \log_{1.025}2$, which can be rewritten using the change of base formula as $n = \frac{\log 2}{\log 1.025}$. Calculating this gives approximately 28.1, meaning it takes about 28.1 quarters to double the investment.

The Number of Quarters Needed to Double an Investment When n=log⁡1.0252n = \log 1.025^2n=log1.0252

The Number of Quarters Needed to Double an Investment When $n = \log 1.025^2$