### Time Value of Money

1) A store offers two payment plans. Under the installment plan, you pay 20% down and 20% of the purchase price in each of the next 4 years. If you pay the entire bill immediately, you can take a 5% discount from the purchase price.| a.| Calculate the present value of the payments, if you can borrow or lend funds at a 7% interest rate. Assume the product sells for \$100. (Do not round intermediate calculations. Round your answer to 2 decimal places.)| Present value| \$ |

b.| Calculate the payment net of discount.|
Payment net of discount| \$ |
c.| Which is a better deal?|
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| | Pay the entire bill immediately|
| Installment plan|
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2) Home loans typically involve “points,” which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if the loan is for \$170,000 and 4 points are charged, the loan repayment schedule is calculated on a \$170,000 loan but the net amount the borrower receives is only \$163,200. What is the effective annual interest rate charged on such a loan assuming loan repayment occurs over 156 months? Assume the interest rate is .75% per month. (Do not round intermediate calculations. Round your answer to 2 decimal places.)| Effective annual interest rate| % |

3) Suppose you take out a \$1,000, 4-year loan using add-on interest with a quoted interest rate of 23.25% per year.|

a.| What will your monthly payments be? (Total payments are \$1,000 + \$1,000 × .2325 × 4 = \$1,930.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)|

Monthly payments| \$ |

b.| What are the true APR and effective annual rate on this loan? (Do not round intermediate calculations. Round your answers to 3 decimal places.)|

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APR| % |
Effective annual rate| % |
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4) In a discount interest loan, you pay the interest payment up front. For example, if a 1-year loan is stated as \$28,000 and the interest rate is 22.25%, the borrower “pays” 0.2225 × \$28,000 = \$6,230 immediately, thereby receiving net funds of \$21,770 and repaying \$28,000 in a year. What is the effective annual rate on a 1-year loan with an interest rate quoted on a discount basis of 22.25%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)|

Effective annual rate| % |

5)
You believe you will need to have saved \$520,000 by the time you retire in 40 years in order to live comfortably. If the interest rate is 5% per year, how much must you save each year to meet your retirement goal? (Do not round intermediate calculations. Round your answer to 2 decimal places.)|

Annual savings| \$ |

6)

Your consulting firm will produce cash flows of \$110,000 this year, and you expect cash flow to keep pace with any increase in the general level of prices. The interest rate currently is 6.2%, and you anticipate inflation of about 2.2%.|

a.| What is the present value of your firm’s cash flows for years 1 through 6? (Do not round intermediate calculations. Round your answer to 2 decimal places.)|

Present value| \$ |

b.| How would your answer to (a) change if you anticipated no growth in cash flow? (Do not round intermediate calculations. Round your answer to 2 decimal places.)|

Present value| \$ |

7)
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Good news: You will almost certainly be a millionaire by the time you retire in 40 years. Bad news: The inflation rate over your lifetime will average about 2.6%.|

a.| What will be the real value of \$1 million by the time you retire in terms of today’s dollars? (Do not round intermediate calculations. Round your answer to the nearest dollar amount.)|

Real value| \$ |

b.| What real annuity (in today’s dollars) will \$1 million support if the real interest rate at retirement is 2.4% and the annuity must last for 10 years? (Do not round intermediate calculations. Round your answer to the nearest dollar amount.)|

Real annuity| \$ |

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8)
You believe you will spend \$40,000 a year for 20 years once you retire in 40 years. If the interest rate is 6% per year, how much must you save each year until retirement to meet your retirement goal? (Do not round intermediate calculations. Round your answer to 2 decimal places.)|

Annual savings| \$ |