Question

You are planning to purchase a house that costs $480,000. You plan to put 20% down and borrow the remainder. Based on your credit score, you believe that you will pay 3.99% 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 $1700 per month. What is the most that you can borrow?
3. Use function “RATE” to calculate the interest rate given a payment of $1700 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 or not you should save some of your money and put 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).
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

Principal borrowed = cost of the house - down payment = 480,000 - (20%*480,000) = 384,000

1). Mortgage payment per month: FV = 384,000; N = 30*12 = 260; I = 3.99%/12 = 0.305%, solve for PMT. PMT = 1,758.81

2). Loan amount borrowed: PMT = 1,700; N = 30*12 = 260; I = 3.99%/12 = 0.305%, solve for PV. PV = 371,159.99 or 371,160

3). Interest rate: PV =-384,000; N = 360; PMT = 1,700, solve for RATE. RATE = 0.282% (per month) so annual interest rate = 0.282%*12 = 3.39%

4, 5).

	Number of payments (N)	Loan (P)	Monthly payment (M)	Total payment (T = N*M)	Total interest paid (T-P)	Total cost (including down payment) (TC)	Down payment (D = TC-P)	Total cost of home purchase (D+T)
Scenario 1	360	3,84,000	1,758.81	6,33,171.70	2,49,171.70	4,80,000	96,000	7,29,171.70
Scenario 2	360	3,71,160	1,700.00	6,12,000.00	2,40,840.00	4,80,000	1,08,840	7,20,840.00
Scenario 3	360	3,84,000	1,700.00	6,12,000.00	2,28,000.00	4,80,000	96,000	7,08,000.00

6). P = 384,000; PMT = -(1,758.81 + 300) = -2,058.81; I = 0.305%, solve for NPER. NPER = 276.27 or 277 months = 23.02 years. Compared to part 1), loan will be paid off, almost 7 years earlier.