OK, this reply raves on a bit.. you know how maths people can't stop once they start... so non-interested parties should skip to the next post...

Here goes:

They're just trying to put in a few twists and turns in the question to try to see if you can think clearly. You just need to break the question down into 3 steps:

[Remember that when the question specifically tells you that the interest rates are 'compounding monthly', it wants you to work in months, so use the interest rate per month (the annual interest rates divided by 12) and the monthly payments in your annuity calculations.]

Step 1 - Try to work out the monthly payment for a loan of $150000 using an annuity function for 240 (12*20yrs) months at 0.54% (6.5%p.a./12) of interest per month.

Step 2 - This is, in effect, finding the new monthly payment at the higher interest rate that will maintain the same present value of future payments at 1/9/99.

Work out the new monthly payment after 10 yrs at 1/9/99 by equating the original monthly payment from Step 1 times the annuity function for 120 months at the old interest rate per month against the unknown new monthly payment times the annuity function for the same 120 months at the new monthly interest rate.

Step 3 - This is also trying to maintain the same present value of future payments at a certain date (this time, another 4 yrs later) by varying something else (this time, the question changes the monthly payment) by finding the new remaining term of the loan.

Find the number of months that still need to be paid after Mildred goes back to work at August 2002 (14 years after the start of the loan), by equating the new monthly payment from Step 2 times the annuity function for the 72 months remaining at the new interest rate used in Step 2 against the final monthly payment of $1230 times the annuity function for the unknown number of months at the same new interest rate used in Step 2.

Here's the easy part..

You know that the whole term of the loan was 20 yrs (240 months).

From Step 3, you've also got the actual term of the loan (after all those painful adjustments of interest rate, instalment amounts and term) by adding 120 mths (10 yrs) + 48 mths (4 yrs) + Part 3 answer in months.

Wah-la!! The difference is the answer in months!

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