Question

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?

		$400.00
		$1,185.36
		$1,569.85
		$2,909.17

Answer 1

This question requires application of time value of money concept - concept of FV of annuities.

Basically,

FV of 40 yr annuity of Jane = FV of 20 Yr annuity of Hal

FV of an annuity is mathematically represented as:

r = 8%/12 (monthly)

For Jane,

n = 40 * 12 = 480 months, P = $400

For Hal.

N = 20 * 12 = 240 months, we need to calculate P.

Putting these values in mathematical relation,

1,396,403.13 = P * 589.0204

P = $2,370.72 --> Monthly installment that Hal should save in account to catch up with Jan after 20 years.