Question

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

2.Hank purchased a $20,000 car two years ago using an 8 percent, 5-year loan. He has decided that he would sell the car now, if he could get a price that would pay off the balance of his loan. What is the minimum price Hank would need to receive for his car?

3.Assume that you contribute $300 per month to a retirement plan for 25 years. Then you are able to increase the contribution to $500 per month for 20 years. Given a 9 percent interest rate, what is the value of your retirement plan after 45 years?

Answer 1

Question 1)

Given

Monthly income P=$3000

Interest rate per year=7%

Interest rate per month r=7%/12=0.58%

Years for income =30 years

Number of Income N=30*12=360 months

So Present value of Income PV=P*(1-(1+r)^-N)/r =3000*(1-(1+0.58%)^-360)/0.58%

PV=$450922.70

Ley X be the monthly contribution

Years to retirement =20 years

Number of contribution T=20*12=240 months

r=0.58%

So Future value of Contribution FV= X*((1+r)^T-1)/r

FV=X*((1+0.58%)^240-1)/0.58%=520.93X

Since FV=PV

520.93X=450922.70

X=$865.62