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# Present and Future Values of Annuities

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Answer each of the following independent questions

1. Alex Meir recently won a lottery and has the option of receiving one of the following three prizes.

(1) 64,000 cash immediately,
(2) \$20,000 cash immediately and six-period annuity of \$8,000 beginning one year from today,
(3) a six period annuity of \$8,000 beginning one year from today, or
(4) a six year period annuity of \$13,000 beginning one year from today.

Assuming an interest rate of 6%, which option would Alec choose?

2. The Weiner Corporation wants to accumulate a sum of money to repay certain debts due on December 31, 2020. Weiner will make annual deposits of \$100,000 into a special bank account at the end of each of 10 years beginning December 31, 2011. Assuming that the banks pays 7% interest compounded annually, on December 30, 2014 what will be the fund balance after the last payment?

#### Solution Summary

This solution responds to two questions. First, it illustrates how to evaluate alternative payout options by computing the present values of several annuities and comparing those to a lump-sum. It then illustrates how to compute the future value of an annuity.

\$2.19

## Need Help with formulas on problems

These are just exercises. I need help with figuring out the formulas on all 5 questions.

Thanks!

(Complete problem also found in attachment)

1. 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?

2. Annuity Due. Recall that an annuity due is like an ordinary annuity except that the first payment is made immediately instead of at the end of the first period.

a. Why is the present value of an annuity due equal to (1 + r) times the present value of an ordinary annuity?

b. Why is the future value of an annuity due equal to (1 + r) times the future value of an ordinary annuity?

3. Annuity Due Value. Reconsider the previous problem. What if the lease payments are an annuity due, so that the first payment comes immediately? Is it cheaper to buy or lease?

4. Bond Yields. An AT&T bond has 10 years until maturity, a coupon rate of 8 percent, and sells for \$1,100.
a. What is the current yield on the bond?
b. What is the yield to maturity?

5. Bond Pricing. A General Motors bond carries a coupon rate of 8 percent, has 9 years until maturity, and sells at a yield to maturity of 7 percent.
a. What interest payments do bondholders receive each year?
b. At what price does the bond sell? (Assume annual interest payments.)
c. What will happen to the bond price if the yield to maturity falls to 6 percent?

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