Question

please answer in excel

PART 1

You are planning to purchase a house that costs $420,000. You plan to put some money down and borrow the remainder with a 30-year mortgage.

1. Based on your credit score, you believe that you will pay 3.50% interest if you put 20% down. Use function “PMT” to calculate your mortgage payment.
2. Based on your credit score, you believe that you will pay 3.50% interest. Use function “PV” to calculate the loan amount given a payment of $1,500 per month. What is the most that you can borrow?
3. Use function “RATE” to calculate the interest rate given a monthly payment of $1,500 and a loan amount of $336,000.
4. For each scenario, calculate the total amount of money you will pay. (Down payment plus principle (loan amount) plus interest, or, down payment plus monthly payment times number of payments). Suppose in case 2, you borrow the most that you can borrow, and put down the rest to buy the house.
5. 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.)
6. Assume that you plan to pay an extra $300 per month on top of your $1,500 monthly payment, use function “NPER” to calculate how long it will take you to pay off the $336,000 loan given the higher payment. Assume under this scenario you will pay 3.50% interest. (This should be different from 30 years). Calculate how much interest you will pay in total. Compare this to the value that you calculated for #1.

PART 2

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 annual cost of PMI is 0.8% of the mortgage loan amount that you borrow today. Assume that you will pay PMI for 8 years before you are eligible to waive it.

1. Calculate your total monthly payment for the first 8 years (mortgage payment plus PMI) and the rest 22 years (only mortgage payment).

Monthly cost for PMI = annual cost of PMI/12

2. Calculate the total amount of money you will pay. (Down payment plus principle (loan amount) plus interest plus PMI.)
3. Calculate the total cost of financing of your home purchase (interest plus PMI).
4. Compare this to the total amount of money you will pay associated with a 20% down payment (use data from #1).

Answer 1

Monthly mortgage payment is calculated using PMT function in Excel :

rate = 3.50% / 12 (converting annual rate into monthly rate)

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

pv = 420,000 * 80% (loan principal amount = cost of house * (1 - down payment %)

PMT is calculated to be $1,508.79

Total amount of money you will pay = down payment + (PMT * NPER) = ($420,000 * 20%) + ($1,508.79 * 30 * 12) = $627,164

Total interest paid = Total amount of money you will pay - cost of house = $627,164 - $420,000 = $207,164

Loan amount is calculated using PV function in Excel :

rate = 3.50% / 12 (converting annual rate into monthly rate)

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

pmt = -1500 (monthly payment. This is entered as a negative number because it is a cash outflow)

PV is calculated to be $334,042

Total amount of money you will pay = down payment + (PMT * NPER) = ($420,000 - $334,042) + ($1,500 * 30 * 12) = $625,958

Total interest paid = Total amount of money you will pay - cost of house = $625,958 - $420,000 = $205,958

Interest rate is calculated using RATE function in Excel :

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

pmt = -1500 (monthly payment. This is entered as a negative number because it is a cash outflow)

pv = 336,000 (loan amount)

RATE is calculated to be 0.29%. This is the monthly rate. To calculate annual rate, we multiply by 12. Annual interest rate = 0.29% * 12 = 3.45%

Total amount of money you will pay = down payment + (PMT * NPER) = ($420,000 - $336,000) + ($1,500 * 30 * 12) = $624,000

Total interest paid = Total amount of money you will pay - cost of house = $624,000 - $420,000 = $204,000

Number of months taken to pay off mortgage is calculated using NPER function in Excel :

rate = 3.50% / 12

pmt = -1800 (monthly payment = 1500 + 300)

pv = 336,000

NPER is calculated to be 270 months

In years, this is 270 / 12 = 22.50 years

The mortgage is paid off in 22.50 years instead of 30 years as per the original mortgage

Total amount of money you will pay = down payment + (PMT * NPER) = ($420,000 - $336,000) + ($1,800 * 270) = $570,000

Total interest paid = Total amount of money you will pay - cost of house = $570,000 - $420,000 = $150,000