This page contains suggestions and clarifications for some of the more difficult problems for the second recitation. It does not contain very many final answers.

Problem 6 - 15

Part (a) is very straight forward. She makes 60 deposits of $500 starting one period from now. Simply find the future value of this 60 period annuity of $500 compounded at 5%. The answer is $176,791.86.

Part (b) is more confusing but not really harder. The easiest way to get the answer is to subtract from the answer to (a) the $10,000 and the amount of interest she would have earned on the $10,000 over the remaining 10 years (or actually 20 semi-annual periods). The $10,000 would have grown to $26,532.98 after compounding for 20 periods at 5% interest. The final answer is 500 x (FVIFa - 5% - 60) - 10000 x (1.05)20 = 150,258.88.

Problem 6 - 17

This is how I interpreted the problem: she makes 40 deposits of D dollars starting one year from now. The future value of those 40 deposits (AT AGE 62) compounded at 7% must EXACTLY equal the present value of all the withdrawals (AT AGE 62) she intends to make discounted at 5%. The secret to nearly all of these problems is to pick a point in time that makes sense to you and take all amounts to that point. Set the future value of the 40 D's equal to the present value of the 20 $70,000 withdrawals plus the $120,000 vacation withdrawal. The value of all the withdrawals at age 62 total 120,000 + the present value of the 70,000 annuity for 20 periods discounted at 5%.

The final equation is: D x (FVIFa - 7% - 40) = 120,000 + W x (PVIFa - 5% - 20). Solve for D.

Problem X - 3

Let's do the calculations for your brother's loan. Find the interest rate per period where a period is one quarter. 10000 is the present value of the loan because that is what he's borrowing today. 1004.62 is the payment per period. 12 is the number of payments. Set the present value of the 12 payments equal to the 10,000 and solve for the interest rate that equates the two. It should be 3.00% per quarter. Convert this to a meaningless APR and the all important EAR. Repeat for your sister and then decide which is a better deal for you.