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# Calculate the annual payment on a loan using the present value of an annuity.

This assignment will allow you to demonstrate the following objectives:

· Calculate the annual payment on a loan using the present value of an annuity.

· Use discounting to determine the present value of an annuity.

· Calculate the future value of an annuity and periodic annuity payments.

· Determine the present value of a bond.

Instructions: Answer the questions directly on this document. When you are finished, select “Save As,” and save the document using this format: Student ID_UnitIV. Upload this document to BlackBoard as a .doc, docx, or .rtf file. Show all of your work.

1. Your supervisor has tasked you with evaluating several loans related to a new expansion project. Using the PVIFA table (table 9.4 in the textbook), determine the annual payment on a \$400,000, 8% business loan from a commercial bank that is to be amortized over a five-year period. Show your work. Does this payment seem reasonable? Explain.

Table 9.4 shows PVIFA values for a partial range of interest rates and time periods. (Table 4 in the Appendix is a more comprehensive PVIFA table.) Let’s use Table 9.4 to find the present value of an ordinary annuity involving annual payments of \$1,000, an 8% interest rate, and a three-year time period. Notice that at the intersection of the 8% interest rate column and three years we find a PVIFA of 2.577. Putting this information into equation 9.8 gives,

PVA = \$1000 (2577)

= \$2577

Further examination of Table 9.4 shows how the present value of a \$1 annuity decreases with various combinations of interest rates and time periods. For example, if \$1,000 is paid at the end of each year (beginning with year one) for ten years at an 8% interest rate, the present value of the annuity would be \$6,710 (\$1,000 × 6.710). If the interest rate is 10% for ten years, the present value of the annuity would be \$6,145 (\$1,000 × 6.145). These results demonstrate the costs of higher interest rates on the present values of annuities.

2. Dan is considering borrowing \$500,000 to purchase a new condo. Based on that information, answer the following questions. Show all work.

a) Calculate the monthly payment needed to amortize an 8% fixed-rate 30-year mortgage loan.

b) Calculate the monthly amortization payment if the loan in (a.) was for 15 years instead.

3 Use a financial calculator or computer software program to answer the following questions:

a) Melanie is trying to save money for retirement and has a future goal of \$600,000 at the end of 20 years. Determine the present value of her goal using a discount rate of 11%.

b) How would the present value change if the \$600,000 is to be received at the end of 15 years instead? Explain the impact and show your work?

4. Your friend Anne is planning to invest \$400 each year for four years and will earn a rate of 6 percent per year.

a) Determine the future value of this annuity due if her first \$400 is invested now. Show your work.

b) What is the difference between an annuity due and an ordinary annuity? Explain.

5. Jimmy has a bond with a \$1,000 face value and a coupon rate of 9.5% paid semiannually. It has a five-year life.

a) If investors are willing to accept a 14 percent rate of return on bonds of similar quality, what is the present value or worth of this bond? Show your work.

b) What is the impact of paying interest semi-annually rather than annually? Explain.

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Approximately 250 words
\$12