Acme Annuities recently offered an annuity that pays 4.5 % compounded monthly. What equal monthly deposit should be made into this annuity in order to have $ 131,000 in 13 ​years?

Acme Annuities recently offered an annuity that pays 4.5 % compounded monthly. What equal monthly deposit should be made into this annuity in order to have $ 131 comma 000 in 13 ​years?

Information given:

Interest rate per year =4.5%

Change it to decimal and monthly.

To get interest rate in decimal, divide 4.5% by 100. We get 0.045.

To get monthly interest rate divide it by 12 because we have 12 months in a year.

So, interest rate per month in decimal =0.045/12=0.00375

Now, the goal amount is $131000.

Number of years is 13.

What to find?

We need to find the monthly payment amount Pmt, using the given information.

Formula to be used:

Pmt = (rA)/((1+r)^N-1))

A is amount of goal.

r is rate of interest per period in decimal.

N is number of times compounded in 13 years.

We know r=0.00375

A=131000

N=13*12=156 (because there are 12 months in a year).

Steps of solving:

Plug in these values into the formula.

Pmt= ((0.00375)(131000))/((1+0.00375)^156  -1)

Simplify it

Pmt =(491.25)/(0.793028087)

Simplify it further.

Pmt =$619.46

Answer:

Monthly payment is $619.46.

 

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