math problem payment size

label Mathematics
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Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 6%/year compounded monthly. If the future value of the annuity after 13 yr is $70,000, what was the size of each payment? 

Dec 9th, 2014

Use the Future Value of Ordinary Annuity Formula


FV = A × [(1 + r)^n - 1]/r

Where,

FV = future value of ordinary annuity

A = annuity payment 

r = interest rate

n = number of time periods


In this case,

FV = $70,000

A = annuity payment 

r = .06/12 = .005 (divide interest rate by 12 since it is compounded monthly)

n = 13 * 12 = 156 (multiply number of years by 12 since compounded monthly)


70000 = A × [(1 + .005)^156 - 1]/.005     plug in known variables

70000 = A × [(1.005)^156 - 1]/.005         simplify 

70000 = A × [(2.17724- 1]/.005               simplify

70000 = A × 1.17724/.005                       simplify

70000 = A × 235.44733                           simplify

A = 70000/235.44733                              solve for A

A = $297.31


I hope this helps. Good Luck!


Dec 10th, 2014

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Dec 9th, 2014
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