Use your calculator to determine (1) the current mortgage payment (2) the total

Question

Use your calculator to determine (1) the current mortgage payment (2) the total interest paid, (3) the payment after the first adjustment and (4) the maximum payment for the following $156,000, 30-year mortgage. Assume that the initial interest rate is 6.90 percent.

a. Fixed for 3 years and then annually adjustable, 2 percent per year, 5 percent lifetime cap. Assume also that rates increase at least 2 percent per year until they reach the lifetime cap and rates never again drop below the lifetime cap for the term of the mortgage.

This is from the first part of the question.

(Annually adjustable, 1 percent per year, 5 percent lifetime cap. Assume also that rates increase at least 1 percent per year until they reach the lifetime cap and rates never again drop below the lifetime cap for the term of the mortgage.)

Explanation / Answer

Monthly Mortgage Payment formula = Loan * [r * (1+r)t ] / [(1+r)t - 1]

Resiual Loan balance after k months = Loan * [(1+r)t - (1+r)k ] / [(1+r)t - 1]

r is the applicable monthly interest rate and t is the amortisation term in months

We are given :

Loan Amount = 156000; r = 6.90% per annum or monthly 0.58% ; Term = 360 months

1. Current Mortgage Payment = 156000 * [0.58% *(1+0.58%)360] / [(1+0.58%)360 - 1] = 1027.42

2. Total interest paid = (1027.42 * 360) - 156000 = 213869.83

3. The loan amount at the end of 3 years (36 months) = 156000 * [(1+0.58%)360 - (1+0.58%)36] / [(1+0.58%)360 - 1] = 150800.3

Monthly mortgage rate at 8.90% (adjusted rate) with residual renure of 27 years =

150800.3 * [0.74% *(1+0.74%)324] / [(1+0.74%)324 - 1] = 1230.74

4. The interest rate in Year 4 is 8.90%, Year 5 is 10.90 and from Year 6 onwards capped at 11.90%

Loan Balance at the end of Year 4 = 150800.3 * [(1+0.74%)312 - (1+0.74%)12] / [(1+0.74%)312 - 1] = 149251.6

Loan Balance at the end of Year 5 = 149251.5 * [(1+0.91%)300 - (1+0.91%)12] / [(1+0.91%)300 - 1] = 148035.8

Monthly mortgage payment at highest rate (11.90%) from Year 6 * [0.99% *(1+0.99%)288] / [(1+0.99%)288 - 1] = 1558.93 which is the highest monthly payment for this loan

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