Question

Mortgage Analysis

You are planning to purchase a house that costs $4 80,000. You plan to put 20% down and borrow the remainder. Based on your credit score, you believe that you will pay 3.25% on a 30-year mortgage.

1. Use function “PMT” to calculate your mortgage payment.
2. Use function “PV” to calculate the loan amount given a payment of $1550 per month. What is the most that you can borrow?
3. Use function “RATE” to calculate the interest rate given a payment of $1550 and a loan amount of $384,000.
4. For each scenario, calculate the total interest that you will have paid once the mortgage is paid off. (There is not a function for this, enter the formula into the cell.)
5. For each scenario, calculate the total cost of the home purchase. (Down payment plus principle (loan amount) plus interest.)
6. Assume that you plan to pay an extra $300 per month on top of your mortgage payment, calculate how long it will take you to pay off the loan given the higher payment. (Use the data from #1). Calculate how much interest you will pay in total? Compare this to the value that you calculated for #1.

You want to determine whether you should only 10% down on your house. Because you are only putting 10% down, lenders require that you purchase private mortgage insurance (PMI). Assume that PMI is 1% of the mortgage amount. Assume that you will pay PMI for 8 years in total (the assumption is that you will have 20% equity at that time so PMI will no longer be needed).

7. Calculate your total monthly payment (mortgage payment plus PMI).
8. Calculate the total cost of financing your home purchase (interest plus PMI). (remember that you only pay PMI for 8 years)
9. Calculate the total cost of the home purchase. (Down payment plus principle (loan amount) plus interest plus PMI.)
10. Compare this to the costs associated with a 20% down payment (use data from #1).

Answer 1

#1]

Monthly payment is calculated using PMT function in Excel :

rate = 3.25% / 12   (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pv = 384000 (loan amount = $480,000 * (1 - 20%) = $384,000 )

PMT is calculated to be $1,671.19

#2]

The loan amount is calculated using PV function in Excel :

rate = 3.25% / 12   (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pmt = -1550 (Monthly loan payment. This is entered with a negative sign because it is a payment)

PV is calculated to be $356,152.92

#3]

Interest rate is calculated using RATE function in Excel :

nper = 30*12 (30 year loan with 12 monthly payments each year)

pmt = -1550 (Monthly loan payment. This is entered with a negative sign because it is a payment)

pv = 384000 (loan amount)

RATE is calculated to be 0.22%. This is the monthly rate. To get annual rate, we multiply by 12. Annual interest rate is 2.66%

#4]

With monthly payments of $1,671.19, total interest paid = total payments - loan amount

total interest paid = ($1,671.19 * 30 * 12) - $384,000 = $217,629.22

With monthly payments of $1,550, total interest paid = total payments - loan amount

total interest paid = ($1,550 * 30 * 12) - $384,000 = $174,000