4. Joan borrowed $15000 to buy a car. She repaid $2000 two months later and $5000
seven months later. After twelve months,
she borrowed an additional $4000, and repaid $3000 after 16 months. She paid the entire balance, including the
interest, after 24 months. Interest was
7% compounded monthly for the first year and 7.5% compounded monthly for the
remaining time. What was the size of the
final payment?
How to approach this problem:
1. Draw a timeline with the dates and amounts, just as we do in class.
2. We solve this by 'rolling the money along'. We cannot bring all the amounts to the end date because the interest rate changes.
3. So to begin with, the PV is 15000. Find the FV after two months. At that point, you repay 2000. So subtract 2000 from the FV you have just found. That is what Joan owes after two months. This amount is now the PV for the next stage. So keep going with the same method. Be very careful to note when the interest rate changes.
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