Problem
I. Discount Interest Loans This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $18,000 for one year. The interest rate is 14.6 percent. You and the lender agree that the interest on the loan will be .146 × $18,000 = $2,628. So, the lender deducts this interest amount from the loan up front and gives you $15,372. In this case, we say that the discount is $2,628. What's wrong here?
II. Calculating Annuity Values You are serving on a jury. A plaintiff is suing the city for injuries sustained after a freak street-sweeper accident. In the trial, doctors testified that it will be five years before the plaintiff is able to return to work. The jury already has decided in favor of the plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award to cover the following: (a) The present value of two years' back pay.
The plaintiff's annual salary for the last two years would have been $44,000 and $47,000, respectively. (b) The present value of five years' future salary. You assume the salary will be $51,000 per year. (c) $200,000 for pain and suffering. (d) $25,000 for court costs. Assume that the salary payments are equal amounts paid at the end of each month. If the interest rate you choose is an EAR of 7 percent, what is the size of the settlement? If you were the plaintiff, would you like to see a higher or lower interest rate?
III. Calculating EAR with Points You are looking at a one-year loan of $15,000. The interest rate is quoted as 12 percent plus two points. A point on a loan is 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay two points to the lender up front and repay the loan later with 12 percent interest. What rate would you actually be paying here?
IV. Future Value and Multiple Cash Flows An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or grandparent for a child at the child's birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:
First birthday: $ 800
Second birthday: $ 800
Third birthday: $ 900
Fourth birthday: $ 900
Fifth birthday: $1,000
Sixth birthday: $1,000
After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $150,000. If the relevant interest rate is 10 percent for the first six years and 5.75 percent for all subsequent years, is the policy worth buying?