Question

Your pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). You can afford to put $1,600 per quarter into the fund, and you will work for 40 years before retiring. After you retire, you will be paid a quarterly pension based on a 25-year payout. How much will you receive each quarter? (Round your answer to the nearest cent.)

Answer 1

The cash to receive each quarter is $9,935.32

Step-by-step explanation:

There are two tasks here,the first is the computation of future value of the pension in 40 years' time and thereafter computing the quarterly payment for 25 years when retired.

The future value of the pension can be computed using the fv function in excel,=-fv(rate,nper,pmt,pv)

rate is the quarterly rate of interest i.e 4%/4=1%

nper is the number of times the $1,600 would invested in the fund,that is 40*4=160 times

pmt is the $1,600 inflow into the fund per quarter

pv is not known so is assumed zero

=fv(1%,160,-1600,0)

fv=$626,212.22

Second task:

amount of quarterly payment when retired is computed using pmt formula in excel:

=pmt(rate,nper,-pv,fv)

rate is 1%

nper is 25 years *2=100

pv is the pension value when retired is $626,212.22

note that this amount $626,212.22 was future value in year zero,but a present value in year 40th.

fv is zero

=pmt(1%,100,-626212.22,0)

pmt=$9,935.32