Question

Rodney wants to start saving for a lump-sum amount of $200,000 (in today's dollars) that is needed in five years. He assumes an inflation rate of 3% and a before-tax rate of return of 7% on any investments that are set aside to meet this goal. How much must Rodney deposit at the end of each of the five years using the level payment approach?

A) $40,317.39
B) $28,476.37
C) $37,679.68
D) $41,526.91

Answer 1

To reach his $200,000 goal in today's dollars in five years, accounting for 3% inflation and a 7% investment return, Rodney needs to deposit approximately $28,476.37 annually using the level payment approach.

Step-by-step explanation:

To calculate how much Rodney needs to deposit at the end of each of the five years to reach his $200,000 goal accounting for inflation and investment return, we need to adjust the future value to today's dollars by factoring in inflation and then calculate the annuity payment with the adjusted amount considering a 7% investment return.

Firstly, we adjust the goal amount for 3% annual inflation over 5 years: $200,000 / (1.03)^5. Next, we use the future value of an ordinary annuity formula: PMT = FV / (((1 + r)^n - 1) / r), where PMT is the payment, FV is the future value, r is the annual return rate, and n is the number of periods.

After inflation adjustment, $200,000 in today's dollars is roughly $172,765. Then, we plug in for an annual return of 7% to find the equal annual savings needed.