Question

Consider a two-step mortgage for $150,000, 30 years, monthly payments, an initial interest rate of 5%, a cap of 5%, and a single rate adjustment at the end of year 7. Assume that the index rate at the end of year 7 is 5% and the margin is 2%. If the borrower pays an extra $100 with each payment starting in month 85, by how many months will he shorten the term of the loan

Answer 1

Answer:

Consider the following calculations

Explanation:

This 2-step mortgage problem requires a 2-step solution.

To solve for the PMT for the last 23 years of the loan, we first need to know what the principal is at the end of the 7th year.

Thus, step I uses the initial info to solve for the PMT for each month of the first 7 years. N=360, I/Y=5(%)/12 = 0.416667(%), PV=150,000, => PMT = 805.

The discount rate will change to 5% index rate plus 2% margin = 7% at the beginning of the 8th year.

In Step II we first determine the remaining balance at the end of year 7. This requires using the amortization worksheet.

On the TI BA II Plus, AMORT is the secondary function of PV.

Set P1, the periods at which the calculations begin, equal to 1. We cursor down to P2, which is the last period of the calculation, and set it equal to 84. Cursoring down once again, we see that BAL at month 84 = 131,917.52.  

Going back to the TVM row, we set PV remaining at the end of 23 years = 131,917.52. I/Y is calcluated as 5(%) index rate plus 2(%) margin =7%; dividing 7(%) by 12 = 0.583333(%).  N=360-84 = 276 months left.

Finally, we solve for PMT = 962.89.