In 1980, Jack and Dianne began planning for their retirement in 2025. Jack makes monthly payments of $255 into an annuity paying 5.4% annual interest and Dianne makes monthly payments of $275 into a 403B which pays 4.5% annual interest.
a) In 1994, whose plan had more money in it?
I
b) What will be the value of Jack's retirement plan in 2025 when he retires? $
c) What will be the value of Dianne's retirement plan in 2025 when she retires? $
d) When (what year and what month) will Jack and Dianne have the same amount in their retirement plans? (Hint: graph each function and find
the intersection)

This can be solved by equating the future value of the payment F1, and the future value of the annuity F2, after n=12*15=180 months.

i is the monthly interest.

P=payment of 90000

A=monthly amount of 850

F1=P(1+i)^n=90000(1+i)^180

F2=A*((1+i)^n-1)/i=850((1+i)^180-1)/i

equate F1=F2 and solve for i (only unknown) by trial and error, fix-point iteration or Newton's method to get i=0.00650439,or 0.650439%

The monthly interest rate is 0.650439%.

Therefore the APR=12*i=7.805271%, or the effective interest rate is

(1+i)^12-1=8.09064%

Step-by-step explanation:

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