Question

Ross has decided that he wants to build enough retirement wealth that, if invested at 7 percent per year, will provide him with $3,000 of monthly income for 30 years. To date, he has saved nothing, but he still has 20 years until he retires. How much money does he need to contribute per month to reach his goal

Answer 1

Answer:

he need to contribute per month to reach his goal is $865.61

Explanation:

given data

invested = 7 percent = $\frac{0.07}{12}$

income = $3,000

time = 30 years = 30 × 12 = 360 months

retire = 20 year  = 20 × 12 = 240 months

solution

we get here present value of annuity that is

PVA = $\frac{c\times (1-(1+r)^{-t})}{r}$   ..............1

here c is cash flow i.e $3000 and r is rate and t is time

put here value

PVA = $\frac{3000\times (1-(1+\frac{0.07}{12})^{-360})}{\frac{0.07}{12}}$      

solve it we get

PVA = $450922.70

and

now we get payment of cash flow by PVA in 20 year that is

PVA = $\frac{c\times (1-(1+r)^{-t})}{r}$   ..............2

put here value

$450922.70  = $\frac{c\times (1-(1+\frac{0.07}{12})^{-240})}{\frac{0.07}{12}}$  

solve it we get

c = $865.61