Question

Wenjing purchases a bond for $1,000 with 10 remaining $40 quarterly coupon payments. The bond broker who sells her the bond reassures her that she will earn a return of 5% per quarter but does not disclose the bond's par value. What par value would result in the return the bond broker promises?

Answer 1

The price of the bond (P) having coupon payment (c) and par value (F) at the interest rate of r per period for n periods is,

P = c/(1+r) + c/(1+r)^2 + c/(1+r)^3 +.......+c/(1+r)^n + F/(1+r)^n

=> P = c[(1-1/(1+r)^n)/r] + F/(1+r)^n

(Using the sum of geomertic progression having first term c/(1+r) and common ratio 1/(1+r) )

Here, P = $1000, c = $40, r = 5% and n= 10

=>
1000 = 40[(1-1/(1+0.05)^10 / 0.05] + F/(1+0.05)^10

=> 1000 = 686.363 + F/(1+0.05)^10

=> F = $1125.78

Thus, par value of the bond is $1125.78

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