Q4 from Take Home 1

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.

Chapter 9 Quiz Q4

This question asks: what are the proceeds of a $5000 eight-year note bearing interest at 8%, compounded quarterly, discounted three and a half years after the date of issue at 6% compounded monthly.

Attack: first find the maturity value after eight years. Then discount.

Step 1: maturity value

The PV is 5000
The PY/CY is 4 because the note is compounded quarterly
The N is 8 * 4 = 32
The IY is 8
CPT FV = 9422.7

Step 2: the note was sold off 3.5 years after issue. That means 4.5 years BEFORE the maturity date (because 8 - 3.5 = 4.5). The 4.5 is the date on which we want the present value. Note carefully that we now use the interest rate for the new terms.

FV 9422.7
The PY/CY is 12 because the new interest rate is compounded monthly
The IY is 6
The N is 4.5 * 12 = 54
CPT PV 7197.94

That is the answer: $7197.94