Question

Valerie needs ​$16 comma 000 5 years from now in order to pay off a loan. How much must she save each quarter for the next 5 years if interest rates are 5​% compounded​ quarterly? How much of the ​$16 comma 000 will be​ interest?

Answer 1

Quarterly saving is $709.13

Interest value is $1,817.40

Explanation:

A fix Payment for a specified period of time is called annuity. The Compounding of these payment on a specified rate is known as Future value of annuity.

We can calculate the amount of saving in each quarter Formula for Future value of annuity because we already have future value of $16,000

Future value of annuity = FV = P x ( [ 1 + r ]^n - 1 ) / r

Where

FV = $16,000

r = rate of return = 5%

n = number of years = 5 years 4 quarters each year = 20 quarters

Placing Value in the formula

$16,000 = P x ( [ 1 + 5%/4 ]^20 - 1 ) / 5%/4

$16,000 = P x 22.563

P = $16,000 / 22.563 = $709.13

Interest Amount = Future Value - Total Payment = $16,000 - (709.13 x 20) = $1,817.4