Finance and Algebra

Question

You want to be able to withdraw $50,000 from your account each year for 15 years after you retire. If you expect to retire in 20 years and your account earns 7.9% interest while saving for retirement and 6.2% interest while retired:

a) How much will you need to have when you retire?

b) How much will you need to deposit each month until retirement to achieve your retirement goals?

c) How much did you deposit into you retirement account?

d) How much did you receive in payments during retirement?

e) How much of the money you received was interest?

Answer 1

(a) Cash flow=$50000 r=6.2/100=0.062

n=15yrs

Present value =50,000(1-(1+0.062)^-15/0.062

=$773,339.35484

(b) when future BBCvalue $773,739.3548 in 15 years at a rate of of 7.9,monthly payment will be

(Future value). r/((1+r)^n-1))

r=7.9/100=0.079

Periodic rate monthly=0.079/12=0.00658333

Number of periods=20x12=240 n=240

Monthly payment =773,739.35484(0.0065833)/(1+0.0065833)^240-1

=$1330.0175705332

(c) 1330.0175705332*240=$319,204.21692797

Deposit in retirement account =$319,204.21692791

(d) $50,000*15=$750,000

Payment received during retirement =$750,000

(e) $750,000-319,204.21692791=$430,795.78307209

Interest received =$430,795.78307209