# Present Value Factors and Simple versus Compound Interest

1) Suppose you are trying to find the present value of two different cash flows using the same interest rate for each. One cash flow is $1,000 ten years from now, the other $800 seven years from now. Which of the following is true about the discount factors used in these valuations?

a. The discount factor for the cash flow ten years away is always less than or equal to the discount factor for the cash flow that is received seven years from now.

b. Both discount factors are greater than one.

c. Regardless of the interest rate, the discount factors are such that the present value of the $1,000 will always be greater than the present value of the $800.

d. Since the payments are different, no statement can be made regarding the discount factors.

e. You should factor in the time differential and choose the payment that arrives the soonest.

2)You are choosing between investments offered by two different banks. One promises a return of 10% for three years using simple interest while the other offers a return of 10% for three years using compound interest. You should:

a. Choose the simple interest option because both have the same basic interest rate.

b. Choose the compound interest option because it provides a higher return.

c. Choose the compound interest option only if the compounding is for monthly periods.

d. Choose the simple interest option only if compounding occurs more than once a year.

e. Choose the compound interest option only if you are investing less than $5,000.

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#### Solution Preview

1) Suppose you are trying to find the present value of two different cash flows using the same interest rate for each. One cash flow is $1,000 ten years from now, the other $800 seven years from now. Which of the following is true about the discount factors used in these valuations?

a. The discount factor for the cash flow ten years away is always less than or equal to the discount factor for the cash flow that is received seven years from now.

b. Both discount factors are greater than one.

c. Regardless of the ...

#### Solution Summary

The solution examines the present value factors and simple versus compound interest.

Finance questions

I have attached a format to use for the following questions. I need help, because for some of these I have been searching online for a calculator that can help me an I need help with these and others.

The week 2 word document are the questions and the excel document is the template the have to go in.

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1.Present Values. Compute the present value of a $100 cash flow for the following combinations of discount rates and times:

a. r = 8 percent. t = 10 years.

b. r = 8 percent. t = 20 years.

c. r = 4 percent. t = 10 years.

d. r = 4 percent. t = 20 years.

2. Future Values. Compute the future value of a $100 cash flow for the same combinations of rates and times as in problem 1.

6. Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values:

Present Value Years Future Value

$400 11 $684

$183 4 $249

$300 7 $300

10. Number of Periods. How long will it take for $400 to grow to $1,000 at the interest rate specified?

a. 4 percent

b. 8 percent

c. 16 percent

20. Present Values. A famous quarterback just signed a $15 million contract providing $3 million a year for 5 years. A less famous receiver signed a $14 million 5-year contract providing $4 million now and $2 million a year for 5 years. Who is better paid? The interest rate is 10 percent.

22. Annuity Values.

a. What is the present value of a 3-year annuity of $100 if the discount rate is 6 percent?

b. What is the present value of the annuity in (a) if you have to wait 2 years instead of 1 year for the payment stream to start?

37. Amortizing Loan. Consider a 4-year amortizing loan. You borrow $1,000 initially, and repay it in four equal annual year-end payments.

a. If the interest rate is 8 percent, show that the annual payment is $301.92.

b. Fill in the following table, which shows how much of each payment is interest versus

principal repayment (that is, amortization), and the outstanding balance on the loan at each

date.

Loan Year-End Interest Year-End Amortization

Time Balance Due on Balance Payment of Loan

0 $1,000 $80 $301.92 $221.92

1 --- --- 301.92 ---

2 --- --- 301.92 ---

3 --- --- 301.92 ---

4 0 0 - -

c. Show that the loan balance after 1 year is equal to the year-end payment of $301.92 times the 3-year annuity factor.

39. Annuity Value. The $40 million lottery payment that you just won actually pays $2 million per year for 20 years. If the discount rate is 8 percent, and the first payment comes in 1 year, what is the present value of the winnings? What if the first payment comes immediately?

59. Retirement Savings. You believe you will need to have saved $500,000 by the time you retire in 40 years in order to live comfortably. If the interest rate is 6 percent per year, how much must you save each year to meet your retirement goal?

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