# Calculating: Annuity Values, Annuity Due, Present Value, Future Value, Bond Yields, Bond Pricing and more...

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?

#### Solution Preview

1. Annuity Values.

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

In order to solve these problems, we'll assume here that the flow of payments start 3 year from now, and thus this is like an ordinary annuity (you can use the other formula shown in the link if the first payment actually happens today). The formula for the present value is then:

C * [1-(1+i)^(-n)]

------------------

i

where C is the payment per period ($100 in all cases), i is the interest rate (0.06 for point a) and n is the number of payments =3. So, the present value of this flow of payments is $267.30

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?

We can think of this question in the following way. We're now at the beginning of year 0. In one year (at the beginning of year 1), the annuity payments will start in exactly one more year. Therefore, one year from today (at the beginning of year 1), this annuity will be identical to the one in point a. Therefore, the value of the annuity one year from today will be $267.30. Now, in order to find the value of the annuity today, we simply discount this value by the interest ...

#### Solution Summary

You will find the answer to this puzzling assignment inside...