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?
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
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 further.
Monthly payment is $619.46.