Question

6. A $1000 bond pays coupons at a rate of one-third of the effective annual interest rate. The present value of the coupons agrees with the present value of the redemption amount. Find the price of the bond.

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Answer #1

Par value = 1000
Coupon rate = Effective interest /3 = r/3
YTM = r
Coupon = 1000*r/3

PV of Coupons = PV of Par Value
1000*r/3 * (1-(1+r)-n)/r = 1000/(1+r)n

1000*r/3 *((1+r)n-1)/(r *(1+r)n) = 1000/(1+r)n
(1+r)n-1 = 3
(1+r)n = 4

PV of par value = 1000/(1+r)n = 1000/4 = 250

Price of bond = 250*2 = 500

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