You wish to retire in 15 years, at which time you want to have accumulated enough money to receive an annual annuity of $31,000 for 20 years after retirement. During the period before retirement you can earn 12 percent annually, while after retirement you can earn 14 percent on your money. What annual contributions to the retirement fund will allow you to receive the $31,000 annuity?

$ 5,507.47

Explanation:

There are two steps involved in solving this question ,first we need to determine the present of annuity of $31,000 receivable per year after retirement  at retirement date,then use that to calculate the annual contribution:

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

rate is the rate of interest during retirement which is 14%

nper is the period during which the $31000 would be received which is 20

pmt is the $31000 annuity per year

fv is the future worth of the annuity which is unknown

=-pv(14%,20,31000,0)=$ 205,317.05  

The present value above is the future value of the retirement contributions

annual contribution=pmt(rate,nper,pv,-fv)=pmt(12%,15,0, 205317.05) =$ 5,507.47

i might look it up later.