Due Feb. 21                                    CSC 381                             Thacker

The Corporate Headquarters for Extraneous Accounting Procedures (CHEAP) needs to make an important business decision. CHEAP wants to borrow $100 million in order to finance an important research project. CHEAP has located two potential sources for this money. The first, Mutual United Stock and Corporate Liabilities Exchange (MUSCLE) is willing to loan the $100 million at an annual interest rate which has not yet been negotiated. CHEAP would be expected to repay the loan over 10 years by making 10 equal payments at the end of each year. The other source of money is the Security Home Annuity Refund Kartel (SHARK). SHARK is willing to loan the money to CHEAP at 13 percent annual interest. However, SHARK wishes to be paid only the $13 million in interest at the end of each year for 10 years followed by the repayment of the entire $100 million at the end of the tenth year. In order to have the $100 million at the end of ten years it will be necessary to set up a sinking fund. A sinking fund may be thought of as a kind of savings account to which equal payments are made for a certain amount of time and then the whole balance is paid to a second party, in this case SHARK. In CHEAP's case, it is possible to set up a sinking fund which can earn 10 percent annual interest.

In any event the negotiators at HEAP would like to know what interest rate MUSCLE needs to agree to in order to provide an equivalent deal to that offered by SHARK. Your boss has asked you to answer this question.

The relevant information for this project is contained in the following equations. To compute the payment on a loan, you should use the formula

:

where I is the interest rate A is the amount of the loan, n is the number of payments which need to be made, and p is the amount of each payment. A sinking fund or is governed by the equation:

where I is the interest rate, S is the amount of the sinking fund, n is the number of payments made into the sinking fund, and p is the amount of each payment.

You should write a concise program to carry out this computation. In addition to a listing of the program, you should hand in a report describing your computation, and a conditional recommendation to CHEAP detailing which offer you would choose depending upon the final interest rate negotiated with MUSCLE.