Question

A Treasury bond with a par value of $100 pays semiannual coupons at a rate of 5% per annum, has three years until maturity, and is currently priced at $98. Determine the bond’s continuously compounded yield.

Answer 1

Treasury bond

Par value =100

semiannual coupons at a rate = 5%

three years until maturity

currently priced = 98

.

Answers ;

bonds continuously compounded yield = 5.72%

Explanations

Bonds continuously compounded yield is yield to maturity of the debt.

The yield to maturity of debt is calculated as -

The formula for YTM = (C+ ((P-M) / n)) / ((p+m) / 2)

Here,

C (coupon interest) = Coupon rate * Par value = 5% * $100 = $5/2 = $2.5

P (Par Value ) = $100

M (Market Price) = $98

n (periods to maturity) = 3 years × 2 = 6 periods

By applying values into the formula we get,

YTM = ($2.5 + (($100 - $98) / 6)) / (((($100 - $98) / 2)

YTM = ($2.5 - $.3333 / $99

YTM = $2.8333 / $99

YTM = 0.02861or 2.86%

YTM = 2.86% × 2 = 5.72% Annually