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# Valuing bonds (calculating annual yield-to-maturity and fair

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These are the prices for zero coupon bonds per \$1,000 of face value:
Maturity Price
1 yr \$951.5
2 yr \$895.6
3 yr \$825.4

Show all work and formulae
a) What is the annual yield-to-maturity of each bond if the yield is compounded annually? Show work and formulas

b) Consider the prices of zero coupon bonds above, what is the fair price of a coupon bond that pays a coupon of \$10 at year 1, \$10 at year 2, \$10 at year 3 and repays the principal of \$100 at year 3?

c) What is the annual yield-to-maturity of the coupon bond in b)?

#### Solution Preview

** Please see attached file **

These are the prices for zero coupon bonds per \$1,000 of face value:
Maturity Price
1 yr \$951.50
2 yr \$895.60
3 yr \$825.40

Show all work and formulae
a)      What is the annual yield-to-maturity of each bond if the yield is compounded annually? Show work and formulas

yield to maturity (YTM) = (face value / price) ^ (1/n)- 1
where n= years to maturity
^ means raised to the power of
Face value= \$1,000

Maturity Price YTM
1 \$951.50 5.10% =(\$1,000. / \$951.5)^(1/1)-1
2 \$895.60 5.67% =(\$1,000. / \$895.6)^(1/2)-1
3 \$825.40 6.61% =(\$1,000. / ...

#### Solution Summary

Values bonds by calculating annual yield-to-maturity and fair price.

\$2.19
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## Problems on interest rate and yield to maturity

Interest rate and yield to maturity. You can use excel or financial calculator:

1.    What is the fair value of a 2-year \$100,000 T-note with no coupon payment if the current market interest rate is 10%?
2.    If you obtain a 30 year mortgage loan of \$100,000, find your monthly payment if annual interest rate is 3%, 5%, 10%.
3.    You want to buy a 10% coupon bond with a face value of 100000 that yields 6% to maturity of 5 years. What is the price of the bond you want to buy?

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