Help with finance question

Question

Jack plans to take a 30-year fixed rate, 0 point mortgage at 4.625% to finance 80% of his new house with a monthly payment of $1,200. For simplicity, assume that there are no other fees or costs. Jack would like to take a 20-year second mortgage loan (Home Equity Line of Credit (HELOC)), with an annual rate of 5.615%. If Jack can only make $200 monthly payments for the HELOC, how much does he still need right now for the down payment?

Answer 1

There are a few steps to solve this question. You are looking for the downpayment, and you can determine the amount of mortgages from the data provided, however, you also need to determine what the cost of the house is in the first place.

You are told that the first mortgage will finance 80% of the cost of the house.

Using the TVM keys on your financial calculator, you input the following to find the amount of the first mortgage:

I/Y = 4.625/12 = 0.38, N = 30 * 12 = 360, PMT = -1200, FV = 0, CPT PV = 233,400 (rounded)

Since you know the amount of the first mortgage (PV), and you know that this finances 80% of the purchase price of the house, you can find out that the price of the house is = 233,400/0.8 = $291,750

We now determine how much Jack is borrowing by taking out the second mortgage. We use TVM keys on your financial calculator.

I/Y = 5.615/12 = 0.47, N = 20 * 12 = 240, PMT = -200, FV = 0, CPT PV = 28,802 (rounded)

Now, since you know that the cost of the house is $291,750, and you know the amounts of the two mortgages, you can calculate the amount of the downpayment.

Downpayment = Purchase price of house - Mortgage 1 - Mortgage 2

Downpayment = $291,750 - $233,400 - $28,802 = $29,548.