# Time Value of Money: Annuity Cash Flows

Answer the following questions and complete the following problems, as applicable. Unless otherwise directed, assume annual compounding periods in computational problems.

You may solve the following problems algebraically, or you may use a financial calculator or Excel spreadsheet. If you choose to solve the problems algebraically, be sure to show your computations. If you use a financial calculator, show your input values. If you use an Excel spreadsheet, show your input values and formulas.

Note: In addition to your solution to each computational problem, you must show the supporting work leading to your solution to receive credit for your answer.

1. Would you rather have a savings account that paid 4 percent interest, compounded on a monthly basis, or one that compounded interest on an annual basis. Why?

2. What is an amortization schedule, and what are some of its uses?

3."The interest on your home mortgage is tax deductible. Why are the early years of the mortgage more helpful in reducing taxes than in the later years?" (Cornett, Adair, and Nofsinger, 2012, p. 115).

4.What is the difference between an ordinary annuity and an annuity due?

5. "What is the future value of a $500 annuity payment over five years if interest rates are 9 percent?" (Cornett, Adair, and Nofsinger, 2012, p. 116). Recalculate the future value at 8 percent interest, and again, at 10 percent interest.

6."What is the present value of a $700 annuity payment over four years if interest rates are 10 percent?" (Cornett, Adair, and Nofsinger, 2012, p. 116). Recalculate the present value at 9 percent interest, and again, at 11 percent interest.

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#### Solution Preview

1. Compounded interest is interest paid to you on interest previously earned. From a return standpoint, interest compounded monthly will accrue higher value than annually. For example, $100 that earns 10% interest for one year looks like this:

compounded monthly: $100 x 10%(12 months) = $110.47

compounded annually: $100 x 10% = $110

2. An amortization schedule is a payment plan detailing the interest and principal applied (blended payments). For example, in the early years of a home mortgage loan the majority of payments are applied to ...

#### Solution Summary

This solution is comprised of calculations for present value and future value of annuities. It also touches on compounded interest, amortization schedules, ordinary annuity and annuity due.