Question

Monthly payments of $175 are paid into an annuity beginning on January​ 31, with a yearly...

Monthly payments of $175 are paid into an annuity beginning on January​ 31, with a yearly interest rate of 12 ​%,compounded monthly. Add the future values of each payment to calculate the total value of the annuity on September 1.

On September​ 1, the value of the annuity will be __________

​(Round to the nearest​ cent.)

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Answer #1

Monthly annuity payments beginning on January​ 31 =  $175
Interest rate = 12 ​% compounded monthly
Number of months for which annuity payments were made = 8 months

Calculation of total value of the annuity on September 1

Formula of Future value of Annuity

Where, FV = Future value of Annuity
A= Annuity Payment at end of period
r = Annul rate of Interest
t = Number of years
m = Number of periods on compounding frequency (i.e..,12)  

FV = $175 [(1+0.12/12)^8 -1)] / (0.12/12)
FV = $175 [(1.01)^8 -1)] / (0.01)
FV = $175 [1.0828567 -1] / 0.01
FV = $175 * 8.28567056
FV = $1449.9923 or $1449.99 approx.

Total value of the annuity on September 1 = $1449.99

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