Accumulating a growing future sum Personal Finance Problem A retirement home at Deer Trail Estates now costs $ 191 comma 000. Inflation is expected to cause this price to increase at 6% per year over the 17 years before C. L. Donovan retires. If Donovan earns 9% on his investments, ow large must an equal, end-of-year deposit must be to provide the cash needed to buy the home 17 years from now?

$13,910.42

Explanation:

The price of the house increases by 6% per year for 17 years.

The value at the end of 17 years is;

= 191,000 ( 1 + 6%) ¹⁷

= $514,319.60

Mr Donovan needs to deposit an amount per year at an interest rate of 9% that will earn him $514,319.60 at the end of 17 years.

This makes this an annuity which is calculated as;

Future Value of Annuity = Annuity (( 1 + rate )^ no. of periods - 1 ) / rate

514,319.60 = Annuity ((1 + 9%)¹⁷ - 1)/9%

514,319.60 = Annuity * 36.9737

Annuity = 514,319.60/36.9737

= $13,910.42

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