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A zero coupon bond can be redeemed in 10 years for $2000.How much should you be willing to pay for it now withreturn a) 5% compounded monthly b) 4% compoundedcontinuously.

1 Answer

17 votes
17 votes

The price we would be willling to pay is equivalent to the present value (P) calculated using the discount rate for each case.

The future value (A) is equal to $2000 and the period is t = 10 years.

We can relate the present value with the future value with the formula:


A=P(1+(r)/(m))^(t\cdot m)

a) For this case we have:

r = 0.05

m = 12 (monthly compound)

t = 10 years

A = 2000

Then, we can calculate P as:


\begin{gathered} P=(A)/((1+(r)/(m))^(t\cdot m)) \\ P=(2000)/((1+(0.05)/(12))^(10\cdot12)) \\ P=(2000)/((1.004167)^(120)) \\ P=(2000)/(1.647) \\ P=1214.32 \end{gathered}

The price we would be willing to pay today at this discount rate is $1214.32.

b) In this case, r is r = 0.04 and it is compounded continously. In this case, we have to use another equation for continously compounded interest:


A=P\cdot e^(r\cdot t)

For this case, we have:


\begin{gathered} 2000=P\cdot e^(0.04\cdot10) \\ 2000=P\cdot e^(0.4) \\ P=(2000)/(e^(0.4)) \\ P\approx(2000)/(1.4918) \\ P\approx1340.64 \end{gathered}

The price we would be willing to pay today at this discount rate is $1340.64.

Answer:

a) $1214.32

b) $1340.64

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