Question

Randy Hill wants to retire in 20 years with $1,500,000. If he can earn 10% per year on his investments, how much does he need to deposit each year to reach his goal? Round your answer to the nearest dollar. a) $75,000 b) $37,500 c) $26,189 d) $8,591

Answer 1

To calculate the annual deposit Randy Hill needs to make, we can use the formula for the future value of an ordinary annuity:

\[ FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right) \]

Where:

FV = Future value (desired retirement amount)

P = Annual deposit

r = Interest rate per period

n = Number of periods (years in this case)

Plugging in the given values:

FV = $1,500,000

r = 0.10 (10% per year)

n = 20

\[ $1,500,000 = P \times \left(\frac{(1 + 0.10)^{20} - 1}{0.10}\right) \]

Simplifying the equation:

\[ P = \frac{$1,500,000}{\left(\frac{(1 + 0.10)^{20} - 1}{0.10}\right)} \]

Evaluating the expression:

\[ P \approx $26,189 \]

Therefore, Randy Hill needs to deposit approximately $26,189 each year to reach his goal of $1,500,000 in 20 years. Therefore, the correct answer is c) $26,189.