The purchase price and value of a home are $200,000. A borrower secures an 80% L

Question

The purchase price and value of a home are $200,000. A borrower secures an 80% LTV, 30 year ARM with an initial interest rate of 4% to finance the purchase. Mortgage terms call for annual interest rate adjustments. The lender and borrower agree to use the ten year treasury rate as the index with a 2% margin when the interest rate adjusts. There is a 2% annual rate cap.    

a. What is the monthly payment for the first year and what is the loan balance at the end of the first year?

b. If, when the interest rate adjusts, the treasury rate is 8%, what is the monthly payment for the second ?

Please provide explanation and how you did this using a financial calculator.

Explanation / Answer

Since LTV (Loan to Value) is 80%, the principle amount of loan is 80% * 200,000 = $160,000

Initial Interest rate is 4% and loan is faken for 30 years

a. Calculate monthly installments using the excel formula as follows

=PMT(0.33%,360,-160000,0,0) = $760.18

Here interest rate is entered as monthly interest rate = 4% / 12 = 0.33%

Number of payments = 30 years * 12 = 360

b. First months payment of 760.18, calculate principle and interest component.

Interest Component = 160000 * 0.33% = 528

So principle component paid = 760.18 - 528 = 232.18

So principle amount left at the end of Month 1 = 160000 - 232.18 = 159.767.82

Now Treasury bill rate has increased to 8%, new interest rate would be 8+2 = 10%, but since the annual cap is set as 2%, interest rate cannot increase by more than 2% in any year. So new interest rate would be 4+2 = 6%

Now calculate monthly installment using the excel formula as follows

=PMT(0.5%,359,-159767.82,0,0)

Interest rate is entered as 6%/12 = 0.5%

Number of payments remaining are 360 -1 = 359.

So we get monthly installment as $958.84

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