# A 10-year, $1,000 par value zero-coupon rate bond is to be issued to yield 9 percent. a. What... ## Question: A 10-year,$1,000 par value zero-coupon rate bond is to be issued to yield 9 percent.

a. What should be the initial price of the bond?

b. If immediately upon issue, interest rates dropped to 8 percent, what would be the value of the zero-coupon rate bond?

c. If immediately upon issue, interest rates dropped to 10 percent, what would be the value of the zero-coupon rate bond?

## Answer and Explanation:

Given -

• Par Value = $1,000 • Time (t) = 10 Years • Rate (r) = 9% = 0.09 The price of a zero coupon bond is calculated as follows - • Price of Bond = Face Value / ( 1 + r ) ^ t Or, • Price of Bond = 1000 / ( 1 + 0.09 ) ^ 10 Or, • Price of Bond =$422.41

Scenario 1 - When interest rate drops to 8%

• Price of Bond = Face Value / ( 1 + r ) ^ t

Or,

• Price of Bond = 1000 / ( 1 + 0.08 ) ^ 10

Or,

• Price of Bond = $463.19 Scenario 2 - When interest rate increases to 10% • Price of Bond = Face Value / ( 1 + r ) ^ t Or, • Price of Bond = 1000 / ( 1 + 0.10 ) ^ 10 Or, • Price of Bond =$385.54