Question

A full-time worker aged 25 invests $750 a month in a fund which has an average yearly return of 7.2 % compounded monthly (a) The worker wants to estimate what they will have for retirement when they are 60 years old if the rate stays constant. Assume monthly compounding (b) If the worker makes no further deposits and makes no withdrawals after age 60, how much will they have for retirement at age 69? (a) How much money will the worker have in their fund when they are 60 years old? The worker will have $in their fund when they are 60 years old. (Round to the nearest cent as needed.) (b) If the worker makes no further deposits and makes no withdrawals after age 60, how much will they have for retirement at age 69? The worker will have Sin their fund. (Round to the nearest cent as needed.) ar

Answer 1

a.money he will have at 60 years old:

the amount can be known using future value of annuity:

A*[(1+r)^n-1]/r

here,

A = 750

r=7.2% per year = 7.2%*1/12

=>0.6%

=>0.006.

n = 35 years *12

=>420

amount when they are 60 years old = 750*[(1.006)^420-1]/0.006

=>750*[11.3353621/0.006]

=>750*1889.227

=>$1,416,920.25.

b. at end of age 69.

=> amount at end of age 60 * (1+r)^n

=>here,

r= 0.06

n = 9 years *12 =>108.

=>$1,416,920.25 * (1.006)^108

=>$2,703,505.92.