Question

Your mom is thinking of retiring. Her retirement plan will pay her either $ 200 comma 000 immediately on retirement or $ 280 comma 000 five years after the date of her retirement. Which alternative should she choose if the interest rate​ is: a. 0 % per​ year? b. 8 % per​ year? c. 20 % per​ year?

Answer 1

Answer:

a.  $280,000 after 5 years.

b. $200,000 immediately after retirement.

c.  $200,000 immediately after retirement.

Explanation:

The future value of a $200,000 payment, after 5 years at a rate 'r' is:

$F = 200,000*(1+r)^5$

For each rate 'r', your mom should only choose to receive the $200,000 immediately on retirement if F > $280,000, otherwise she should opt for the $280,000 in 5 years.

a. 0 % per​ year

$F = 200,000*(1+0)^5\\F= \ 200,000$

She should opt for the $280,000 after 5 years.

b. 8 % per​ year

$F = 200,000*(1+0.08)^5\\F= \ 293,865.62$

She should opt for the $200,000 immediately after retirement.

c. 20 % per​ year

$F = 200,000*(1+0.2)^5\\F=\ 497,664$

She should opt for the $200,000 immediately after retirement.