Your parents are planning to retire to Tweed Heads,NSW 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

To calculate the amount of savings required, we need to use the future value (FV) formula for annuities:

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

Where:
PMT = the annual end-of-year deposit
r = the interest rate per period (in this case, 10% per year)
n = the number of periods (in this case, 20 years)

First, we need to calculate the future price of the house after 20 years of 4% annual inflation:

Future price = $200,000 x (1 + 4%)^20 = $528,268.82

Now, we can use this amount as the FV and solve for PMT:

$528,268.82 = PMT x [(1 + 10%)^20 - 1] / 10%

PMT = $7,650.94

Therefore, the annual end-of-year deposit required to save enough for the house in 20 years is $7,650.94. Answer B is the best choice.

Your Parents Are Planning to Retire to Tweed Heads,NSW in 20