Question

You and your lovely and/or handsome spouse have decided the purchase a new home with a loan for $260,000. The mortgage you chose offers a contract rate of 4.5%, a maturity of 30 years, and requires the payment of 3 points. What is the annual effective cost of borrowing for this loan if you make your scheduled payments for the full 30 years?

Answer 1

Your lender has offered you a $260,000 mortgage at 4.5% interest. The lender charges 3 mortgage points or 3 discount points

1 discount point in this mortgage is $ 2,600 (1% of $ 260,000) Hence 3 discount points is 3 x $ 2,600 = $ 7800

Adding this to the loan amount gives us $267,800, which at 4.5 % interest would produce a monthly payment of $1356.9.

We calculate the monthly payment by using the Excel spreadsheet. In Excel, the function for calculating the monthly payment is PMT. We need three variables. These are rate of interest (rate), number of periods (nper) and, lastly, the value of the loan or present value (pv).

The formula which you can use in excel is:

=PMT(rate,nper,pv).

Assuming the Contract rate mentioned here is the annual rate of 4.5%

It must be noted that the rate used in the formula should be the monthly rate, that is, 4.5%/12=0.375% or 0.00375

The number of periods represents the number of EMIs.

=PMT(0.045/12, 30*12, 267,800)= 1356.9

The result will come in negative or red, which indicates the cash outflow of the borrower. Here it is $1356.9 monthly outflow.

Now we use this monthly payment figure and use this to find the interest rate as below

If we again use excel to find out the rate using the formula = rate(nper,pmt,pv) where nper = 360, PMT is - 1356.9 and loan value of reset to $260,000 the rate comes out to be 0.3962%

Remember this rate is monthly. If we multiply by 12 the effective annual interest rate comes out to be 12 x 0.3962% = 4.75%

Ans : Annual Effective Cost of borrowing is 4.75%

Thus we see in this example that the effective annual cost of borrowing 4.75% is more than the contract rate of 4.5%.

Changing the loan amount in the calculator back to $200,000, and trying out a few interest rates, shows that an interest rate of 4.11% would produce that same $968 monthly payment. Therefore this loan's effective interest rate, or APR, is 4.11%.