# Retirement Savings, Bond Yields and Coupon Rate

Question 1

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% per year, how much must you save each year until retirement to meet your retirement goal?

Question 2

Bond Yields. An AT&T bond has 10 years until maturity, a coupon rate of 8% and sells for $1,100.

a. What is the current yield on the bond?

b. What is the yield to maturity?

Question 3

A General Motors bond carries a coupon rate of 8%, has 9 years until maturity and sells at a yield to maturity of 7%.

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%.

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#### Solution Preview

Please see the attached file.

Problem 1

The future value (FV) is $500,000 which is equal to a present value (PV) of $500,000/(1.06^40) = $48,611.09.

The PV of a $1 annuity for 40 years at 6% is equal to: $1/0.06 - $1/(0.06*(1.06^40) = $15.0463 (keep extra digits for accuracy).

To get a PV of $48,611.09 the annual investment needs to be 48,611.09/15.0463 = $3,230.77.

The formula to use in an Excel spreadsheet to ...

#### Solution Summary

This solution looks at several problems: retirement savings, bond yields and coupon rates.