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Present Value and Future Value of Annuities

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How would a manager calculate present value and future value for single amounts, annuities, and uneven streams of cash flow.

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1. The present value for a single amount:
The present Value for a single amount is an amount today that is equivalent to a future payment, or series of payments, that has been discounted by an appropriate interest rate and is calculated as:

(1 + i)^n


PV = Present Value
FV = Future Value
i = Interest Rate Per Period
n = Number of Compounding Periods

2. The present value for an annuity:
Annuities are defined as being a stream of equal cash flows into the future at evenly spaced intervals. The Present Value of an Annuity (PVoa) is the value of a stream of expected or promised future payments that have been discounted to a single equivalent value today. The Present Value ...

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The solution determines the present value and future value of annuities.

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Need Help with formulas on problems

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


(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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