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The Smith family is determined to purchase a $250,000 home without incurring any debt. The family...

The Smith family is determined to purchase a $250,000 home without incurring any debt. The family plans to save $2,500 a quarter for this purpose and expects to earn 6.65 percent, compounded quarterly. How long will it be until the family can purchase a home?

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Expert Solution

We can use the future value of annuity to find the number of years.


Where,
FVA = Future Value of Annuity
A = Annuity
i = rate of interest
n = number of payments or periods

Rate of interest is 6.65%, so i = 6.65% / 4 = 0.016625 (since the payment is quarterly we divide it by 4)

So substituting all the known values in the formula, we get.

taking log10 we get:

Now this value is the number of payments or number of quarters required. To make it into years just divide it by 4.

i.e number of years = 59.3915 / 4 = 14.85 years.

jeff jeffy answered 1 year ago
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