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.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

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

FV = PV x (1 + inflation rate)^n
FV = $200,000 x (1 + 0.04)^20
FV = $441,764.88

This means that your parents need to have $441,764.88 in 20 years to purchase the house.

Next, we can use the formula for the future value of an annuity:

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

where PMT is the annual deposit, r is the interest rate per period, and n is the number of periods.

We know the future value (FV), the interest rate (r), and the number of periods (n), so we can solve for the annual deposit (PMT):

PMT = FV x r/[(1 + r)^n - 1]
PMT = $441,764.88 x 0.10/[(1 + 0.10)^20 - 1]
PMT = $7,650.94

Therefore, your parents need to save $7,650.94 each year in equal annual end-of-year deposits to be able to purchase the house in 20 years.

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