Question

8. You need a 25-year, fixed-rate mortgage to buy a new home for $240,000. Your mortgage bank will lend you the money at a 7.5 percent APR for this 300-month loan, with interest compounded monthly. However, you can only afford monthly payments of $850, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. What will be the amount of the balloon payment if you are to keep your monthly payments at $850?

9. A security is currently selling for $8,000 and promises to pay $1,000 annually for the next 9 years, and $1,500 annually in the 3 years thereafter with all payments occurring at the end of each year. If your required rate of return is 7% p.a., should you buy this security?

10. You are now 25 years old and have just been sold an insurance policy with $10,000 protection on your life. The cost is $170 per year. If you live to age 65, the insurance company will pay you $20,000. Assuming you live to age 65, what portion of the annual cost can be called an investment and what portion of the cost purchased protection? Your required rate of return is 10%. Assume payments are at the end of the year. (Hint: Figure out the annual payments required for the future lump sum payment of $20,000. The remaining payment that you are making must be going towards purchasing protection)

Answer 1

8). PVA = P x [{1 - (1 + r)^-n} / r]

= $850 x [{1 - (1 + 0.075/12)^-(25x12)} / 0.075/12]

= $850 x [{1 - 1.00625^-300} / 0.00625] = $850 x 135.32 = $115,021.67

The monthly payments of $900 will amount to a principal payment of $115,021.67. The

amountof principal you will still owe is:

$240,000 - $115,021.67 = $124,978.33

This remaining principal amount will increase at the interest rate on the loan until the end of

theloan period. So the balloon payment in 25 years, which is the FV of the remaining principal

will be:

Balloon Payment = $124,978.33 x [1 + (0.075/12)]^(25x12)

= $124,978.33 x 1.00625³⁰⁰ = $810,219.57

9). Compute the rate of return implied by the cash flows as:

CF0 = -8000; C01 = 1000; F01 = 9; C02 = 1500;F02 = 3; CPT IRR = 8.403%.

So, the cash flows represent an 8.4% return, but you only require 7% -meaning this is a good

deal. Another way to solve is to compute the NPV of the cash flows assuming I =7%. You will

get NPV = 656.41. Because the NPV > 0, the cash inflows are greater than the cost

(i.e.,thecash outflows). So, again, this is a good investment.

10). First, we need to calculate how much you would have to invest to save 20,000 in 40 years

at 10% interest.

A = 20,000 (PMT, 0.1, 40) = $45.19.

Then you are paying 170 - 45.19 = $124.81 per year for protection.