If $1000 is invested at the end of each year in an annuity that pays 8%, compounded annually, the number of years it takes for the future value to amount to $22,000 is given by $t = \log 1.08^{177}$ Use the change of base
Formula to find the number of years until the future value is $22,000, to the nearest tenth of a year.
A) 67.3 years
B) 72.3 years
C) 65.0 years
D) 74.4 years

Question

Quizplus · Accepted Answer

The correct answer is A.The change of base formula is:$$\log_a b = \frac{\log_c b}{\log_c a}$$Using this formula, we can rewrite the given equation as:$$t = \frac{\log 22000}{\log 1.08}$$Now, we can use a calculator to evaluate this expression:$$t = \frac{\log 22000}{\log 1.08} \approx 67.3$$Therefore, the number of years until the future value is $22,000 is approximately 67.3 years.

If $1000 Is Invested at the End of Each Year t=log⁡1.08177t = \log 1.08^{177}t=log1.08177

If $1000 Is Invested at the End of Each Year $t = \log 1.08^{177}$