Question

You are a homebuilder with excess houses in inventory and the local economy heading towards a recession. In order to stimulate home sales, you offer the following promotion: 1.5% annual interest for the first 3 years of your new mortgage!

You have contracted with a local bank to offer 30-year, fully amortizing mortgages for your buyers at a rate of 3.95% per year with a .8 Loan-to-Value (LTV) ratio.

You have agreed to pay the bank the Present Value of the difference in monthly payments between their rate of 3.95%/year and your “teaser” rate of 1.5%/year.

Your promotion is working, and soon you have a home under contract to sell for $300,000. Using a Discount Rate of 5%/year, what is the amount which you will pay the bank at closing to compensate them for the 3-year teaser interest rate?

Answer 1

LTV Ratio : 0.8

Contract Value : $300,000

Loan Value : $300,000 * 0.8 (LTV) = $240,000

Differential Interest Rate : 3.95% - 1.5% = 2.45%

Discount Factor : 5%

First Year Interest = $240,000 * 2.45% = $5880

Add : two years interest @ 5% on $5880 = $6482.7

Second Year Interest = $240,000 * 2.45% = $5880

Add : one year interest @ 5% on $5880 = $6174

Third Year Interest = $240,000 * 2.45% = $5880

Total Interest Payable to Bank at the end of Third Year = $6482.7 + $6174 + $5880 = $18536.7