4 present value interest factor B u s i n e s s F i n a n c e

Answer the 5 questions below:

**1.** Your supervisor has tasked you with evaluating several loans related to a new expansion project. Using the PVIFA table (below), 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**

**Present Value Interest Factor (PVIFA) for a $1 Ordinary Annuity**

Year | 5% | 6% | 7% | 8% | 9% | 10% |

1 | 0.952 | 0.943 | 0.935 | 0.926 | 0.917 | 0.909 |

2 | 1.859 | 1.833 | 1.808 | 1.783 | 1.759 | 1.736 |

3 | 2.273 | 2.673 | 2.624 | 2.577 | 2.531 | 2.487 |

4 | 3.546 | 3.465 | 3.387 | 3.312 | 3.240 | 3.170 |

5 | 4.329 | 4.212 | 4.100 | 3.993 | 3.890 | 3.791 |

6 | 5.076 | 4.917 | 4.767 | 4.623 | 4.486 | 4.355 |

7 | 5.786 | 5.582 | 5.389 | 5.206 | 5.033 | 4.868 |

8 | 6.463 | 6.210 | 5.971 | 5.747 | 5.535 | 5.335 |

9 | 7.108 | 6.802 | 6.515 | 6.247 | 5.995 | 5.759 |

10 | 7.722 | 7.360 | 7.024 | 6.710 | 6.418 | 6.145 |

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

- Calculate the monthly payment needed to amortize an 8% fixed-rate 30-year mortgage loan.
- Calculate the monthly amortization payment if the loan in (a.) was for 15 years instead.
- In a few sentences, explain the effect of a smaller loan period. How does it influence the monthly payment and interest?

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

- 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%.
- 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.

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

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

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