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Commencement of the loan

Work out and submit the following problems:

Problem 1.

o Mr. Smith tells Mr. Jones that he is to receive an inheritance of $1,000 at the end of three years, but he needs as much money as he can get right now. Mr. Jones normally loans money for which he receives interest at the rate of 10% per year. Mr. Jones has ample opportunity to loan all the money he has available at this rate. If you were Mr. Jones, what is the most you could give to Mr. Smith right now in return for his agreement to give you the $1,000 when he receives it at the end of three years and still earn a 10% rate of return on your investment? What is the most you could you give Mr. Smith right now if his inheritance were $1,331? What is the present value (value at this time) of $1,000 to be received in three years discounted at a 10 percent interest rate? Of $1,331? (Note: This is Problem 7 of the "Mastery Check" in lesson 11.)

o Explain carefully the process by which you decided how much this investment is worth to you. (This problem explores the basic concept of present value–what an investment is worth to you. A clear understanding of this concept will help to solve the rest of the problems in this assignment, and in this course.)

Problem 2. Your rich uncle has offered you a choice of one of the three following alternatives: a single payment of $10,000 right now; eight payments of $2,000 a year, one payment at the end of each year for the next eight years; or a single payment of $24,000 at the end of the eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative? Explain carefully how you arrived at your answers.

Problem 3. Some months ago you negotiated a loan from the bank for $20,000 for the purpose of adding two rooms onto your house. The annual rate of interest (apr) of this loan is 7 percent per year. The loan is a fixed rate loan and is to be repaid in five equal annual installments beginning one year following the commencement of the loan. What will be the amount of each loan payment? Explain carefully how you arrived at your answers.

Problem 4. You have just made the first payment on the loan described in Problem 3, so there are still four annual payments due (each of the amount you calculated in Problem 3), one at the end of each year over the next four years. The bank now makes you an offer to let you pay off the entire loan for a single payment of $16,340. This offer seems convenient for you because your uncle (not the same uncle as in Problem 2) recently died and left you an inheritance of sufficient money to cover this payment. However, you also have opportunities to invest this money in other investments that pay a rate of return of 9 percent per year, some of which pay you back in four equal annual installments. You consider these investments to be essentially risk free. You plan to save or invest this money, but are unsure how to utilize it. Which would you prefer: 1) to take the bank up on its offer and pay off the loan now for a single payment of $16,340, or 2) to invest your money elsewhere at a rate of return of 9 percent per year? Show your figures and explain your reasoning very carefully.

(Remember, the unpaid balance of a loan always equals the present value of the future cash payments due.)

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## Q : Determining the monthly payment

You want to buy a new car for $48,000. The contract is in the form of 60 month annuity due at 7.45% APR. What will be your monthly payment?