Chris purchased a 10 year 100 par value bond where 6% coupons are paid semiannually. Cheryl purchased a 100 par value bond where 6% coupons are paid semiannually. There is no maturity date or redemption value for Cheryl’s bond. Cheryl paid $100 for her bond. The yield for Chris’s bond is 80% of the yield for Cheryl’s bond. How much did Chris pay for his bond?

The amount Chris pay for his bond = $109.44

Explanation:

Given that:

Chris purchased a 10 year 100 par value bond where 6% coupons are paid semiannually. Cheryl purchased a 100 par value bond where 6% coupons are paid semiannually.

The Price of the Cheryl's bond is 6% given that it is purchased at at par value where 6% coupons are paid.

Suppose The yield for Chris’s bond is 80% of the yield for Cheryl’s bond.

Then:

Price of the Cheryl's bond = Present Value of the coupon in perpetuity

∴

Yield=

Yield =0.03

Yield =  3%

The Yield of Chris = 0.8 × 3

The Yield of Chris =  2.4% semiannual  

However;

Present Value of the coupons is:  

PV = 47.21

The PV of the face value =

The PV of the face value =  

The PV of the face value =

The PV of the face value =

The PV of the face value = 62.230

Finally:

The amount Chris pay for his bond =  PV of the coupons + PV of the face value

The amount Chris pay for his bond = 47.21 + 62.230

The amount Chris pay for his bond = $109.44