# Bond Problem

What relationships do you observe between maturity and discount rate and the current price?

Calculate the duration of a $1,000 6% coupon bond with three years to maturity. Assume that all market interest rates are 7%.

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#### Solution Preview

1.

Consider a bond with a 7% annual coupon and a face value of $1,000. Complete the following table.

Years to maturity Yield to maturity Current price

3 5 1,054.61

3 7 1,000

6 7 1,000

9 7 1,000

9 9 879.65

What relationships do you observe between maturity and discount rate and the current price?

The price of the bond is the present value of the interest and the principal. The discounting rate is the YTM. In this questions, the annual interest is $70, principal amount is $1,000.

Case 1 - Years to maturity are 3 and YTM is 5%

Price = 70 X PVIFA (3,5%) + 1,000 X PVIF (3,5%)

We use the PVIFA table for interest since it is an annuity and the PVIF table for principal since it is a lump ...

#### Solution Summary

The solution explains the relationship between maturity, discount rate and the current price and also explains how to calculate the duration of a bond.