Case 1. Car John can afford to spend $500 per month on a car. He figures he need
ID: 2765047 • Letter: C
Question
Case 1. Car
John can afford to spend $500 per month on a car. He figures he needs half of it for gas, parking, and insurance. He has been to the bank, and they will loan him 100% of the car's purchase price.
a) If his loan is at a nominal 12% annual rate over 36 months, what is the most expensive car he can purchase?
b) The car he likes costs $14,000 and the dealer will finance it over 60 months at 12%. Can he afford it? If not, for how many months will he need to save his $500 per month?
c) What is the highest interest rate he can pay over 60 months and stay within his budget if he buys the $14,000 car now?
Case 2. Mortgage
a) Assume mortgage payments of $1000 per month for 30 years and an interest rate of 0.5% per month. What initial principal or PW will this repay?
b) Assume annual mortgage payments of $12,000 for 30 years and an interest rate of 6% per year. What initial principal or PW will this repay?
c) Assume annual mortgage payments of $12,000 for 30 years and an interest rate of 6.168% per year. What initial principal or PW will this repay?
Graphs: For each case (car/mortgage) at least one graph, which you can use to back up your discussion. For example, plot the interest payment + principal payment + balance.
Explanation / Answer
Case 1:
a. The amount ofloan that can be saved for the car = 500/2 = 250. This will be equal to pmt, pmt = 250
The rate = 12% per annum = 12/12 = 1% =0.01 per month
The number of months = nper = 36.
The most expensive car he can purchase =pv(rate,nper,pmt) in excel =pv(0.01,36,250)= $7,526.88
b. The monthly payment for a car worth 14,000 for 60 months at 12% p.a or 1% per month is given by =pmt(rate,nper,pv) =pmt(0.01,60,14000) = 311.42 per months. Hence he cannot afford it
The number of months he has to save $500 to pay $250 for the car loan is =nper(rate,pmt,pv) =nper(0.01,250,-14000) = 82.51 months. Hence he needs to save his $500 for 82.51 months to purchase the car
c. The highest interest rate is given by =rate(nper,pmt,pv) =rate(60,250,14000) = 0.2290% per month.
So the per annum highest interest rate = 0.2290*12 = 2.75%
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