Question

1. You’re interested in buying a new computer, and the Microway Ultra 3000 laptop computer which has a 15.7” display (how much does that thing weigh?) has caught your eye. This computer is pretty expensive, $3500, but you notice the company is offering a special financing plan. For $98 at the end of each month for 48 months, this engineering marvel is yours. What is the nominal annual interest rate (APR) and the effective (monthly compounding) annual interest rate for this loan?

2. Fred and Frieda Finance want to purchase an $180,000 home and have $40,000 as a down payment. They find a 30-year mortgage loan at 7.85% APR. What would the Finances monthly payment be under this loan?

3. Assume $1,100 is the maximum approved monthly mortgage payment that Fred and Frieda Finance (from the last question) could receive, and they still have $40,000 as a down payment on a home.   

1) What is the most expensive home the Finances could afford under an 8% APR 30-year mortgage?

2) What is the most expensive home the Finances could afford under a 7% APR 30-year mortgage?

3) What is the most expensive home the Finances could afford under an 8% APR 15-year mortgage?

Answer 1

1)
PV	$     3,500.00
Period	48	Months
PMT  (Monthly)	$          98.00
FV	0
Type	0
Monthly Rate	1.28%
Annual interest rate (APR)  = 1.28% x 12 months	15.33%
Effective Annual rate = Effect(15.33%,12)	16.458%
2)
Cost of Home	$ 180,000.00
Less: Down Payment	$ (40,000.00)
Loan	$ 140,000.00
Period = 30 x 12	360	Month
Monthly Rate = 7.85%/12	0.65%
Monthly Payment = PMT	$1,012.67
3)
a)
Monthly Payment = PMT	$     1,100.00
Period = 30 x 12	360	months
Rate = 8%/12	0.67%
Loan  = PV	$149,911.84
Add: Down Payment	$   40,000.00
Cost of Home	$189,911.84
b)
Monthly Payment = PMT	$     1,100.00
Period = 30 x 12	360	months
Rate = 7%/12	0.58%
Loan  = PV	$165,338.32
Add: Down Payment	$   40,000.00
Cost of Home	$205,338.32
c)
Monthly Payment = PMT	$     1,100.00
Period = 15 x 12	180	months
Rate = 8%/12	0.67%
Loan  = PV	$115,104.65
Add: Down Payment	$   40,000.00
Cost of Home	$155,104.65