Jane has been saving $200 in her retirement account each month for the last 20 years and plans to continue contributing $200 each month for the next 20 years. Her account has been earning an 8 percent annual interest rate and she expects to earn the same rate for the next 20 years. Her twin brother, Hal, has not saved anything for the last 20 years. Due to sibling rivalry, he wants to have as much as Jane is expected to have at the end of 20 years. If Hal expects to earn the same annual interest rate as Jane, how much must Hal save each month to achieve his goal?
A) $400.00
B) $1,185.36
C) $1,569.85
D) $2,909.17

Question

Quizplus · Accepted Answer

To solve this, we use the future value of an annuity formula for both Jane and Hal. For Jane, who has been saving for 20 years and will save for another 20 years, the future value of her savings can be calculated in two parts: the future value of her current savings and the future value of her future savings. For Hal, who wants to match Jane's amount in 20 years, we calculate how much he needs to save each month using the same future value of an annuity formula, setting it equal to the total future value of Jane's savings. Given the same interest rate and time frame for Hal's savings, the calculation will show that Hal needs to save a significantly higher amount each month to match Jane's savings due to the power of compound interest and the head start Jane has. The correct calculation based on the given interest rate and time frames will show that $1,185.36 is the monthly amount Hal needs to save to match Jane's expected savings in 20 years.

Jane Has Been Saving $200 in Her Retirement Account Each