Question

You plan to purchase a $380,000 house using either a 30-year mortgage obtained from your local savings bank with a rate of 8.20 percent, or a 15-year mortgage with a rate of 7.00 percent. You will make a down payment of 25 percent of the purchase price.

a. Calculate the amount of interest and, separately, principal paid on each mortgage. What is the difference in interest paid?

b. Calculate your monthly payments on the two mortgages. What is the difference in the monthly payment on the two mortgages?

Answer 1

Down Payment = 0.25 * 380,000

Down Payment = 95,000

Loan Amount = 380,000 - 95,000

Loan Amount = 285,000

We will calculate the monthly payment on both the loans:

Loan 1: Local Saving Bank

I = 8.2%

Monthly rate = 8.20%/ 12 = 0.68333%

N = 30 * 12 = 360

FV = 0

PV = 285,000

Using Financial Calculator:

PMT = 2,131.10

Total amount paid = 2,131.10 * 360

Total amount paid = 767,196

Interest Paid = 767,196 - 285,000

Interest Paid = 482,196

Loan 2

I = 7%

Monthly rate = 7%/ 12 = 0.58333%

N = 15 * 12 = 180

FV = 0

PV = 285,000

Using Financial Calculator:

PMT = 2,561.66

Total amount paid = 2,561.66 * 180

Total amount paid = 461,098.80

Interest Paid = 461,098.80 - 285,000

Interest Paid = 176,098.80

Difference in Interest Paid = 482,196 - 176,098.80

Difference in Interest Paid = 306,097.20

Part B:

Difference in monthly payments = 2,561.66 - 2,131.10

Difference in monthly payments = 430.56