Your parents are planning to retire in Phoenix, AZ in 20 years. Currently, the typical house that pleases your parents costs $200,000, but they expect inflation to increase the price of the house at a rate of 4% over the next 20 years. In order to buy a house upon retirement, what must they save each year in equal annual end-of-year deposits if they can earn 10% annually?

Question

Quizplus · Accepted Answer

To calculate the required yearly savings for your parents, we need to use the future value formula for an annuity:

FV = PMT x [(1 + r)^n - 1] / r

Where:
PMT = the yearly savings required
r = the annual interest rate (10%)
n = the number of years (20)

We need to find PMT, so we can rearrange the formula:

PMT = FV x (r / [(1 + r)^n - 1])

First, we need to calculate the future value of the house in 20 years:

FV = $200,000 x (1 + 0.04)^20
FV = $480,658.64

Now we can calculate the yearly savings required:

PMT = $480,658.64 x (0.10 / [(1 + 0.10)^20 - 1])
PMT =  $7,650.94

Therefore, your parents must save $7,650.94 each year in equal annual end-of-year deposits to purchase the house upon retirement. Answer is B.

Your Parents Are Planning to Retire in Phoenix, AZ in 20