Actuarial Outpost Loan Question
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 Financial Mathematics Old FM Forum

#1
07-27-2017, 10:34 PM
 gpecci Member CAS SOA Join Date: Jun 2017 Studying for FM College: The Ohio State University - Junior Posts: 30
Loan Question

Question: A ten-year adjustable rate mortgage loan of 23115 is being repaid with quarterly installments of 1000 based upon an initial interest rate of 12% compounded quarterly. Immediately after the twelfth payment the interest rate is increased to 14% compounded quarterly. The quarterly installments remain at 1000. Calculate the loan balance immediately after the 24th payment.

=23115 * (1.03)^12 * (1.035)^12 - 1000 s angle 12 @ 3% * (1.035)^12 - 1000 s angle 12 @ 3.5%
=13752.39

This solution I understand. However, I tried to solve this question prospectively and got the incorrect answer.
I said the loan balance after the 24th payment = 1000 a angle 16 @ 3.5%
However, this equals 12094.12
#2
07-27-2017, 10:44 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,226

The payment will change after the interest rate increase. This question is much easier to do with calculator functions. Calculate the outstanding balance at the time of the rate change as future value. Input as the new present value and set FV to 0. Reset the interest rate and recalculate the payment to fully payoff the loan over the remaining period. Calculate the outstanding balance at the specified time as a future value.
#3
07-28-2017, 12:18 AM
 gpecci Member CAS SOA Join Date: Jun 2017 Studying for FM College: The Ohio State University - Junior Posts: 30

If the payment changes when the interest rate changes, why is 1000 used for all payments in the correct equation?
#4
07-28-2017, 12:44 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,226

I misread. If the payment stays the same then the number of remaining payments would have to change.
#5
07-28-2017, 12:47 AM
 gpecci Member CAS SOA Join Date: Jun 2017 Studying for FM College: The Ohio State University - Junior Posts: 30

So the way I tried to solve the question would be way too much work.