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Chapter 13: Problem 7

One year ago, you bought a two-year bond for \(\$ 900 .\) The bond has a face value of \(\$ 1,000\) and has one year left until maturity. It promises one additional interest payment of \(\$ 50\) at the maturity date. If the interest rate is 5 percent per year, what capital gain (or loss) would you get if you sell the bond today?

Short Answer

Expert verified
The capital gain obtained from selling the bond today would be $100.

Step by step solution

01

Calculate future value of bond

To calculate the future value (FV) of the bond, it's needed to take into consideration the bond’s face value plus the additional interest payment. Therefore, the FV of the bond is \(1000 + 50 = 1050\)
02

Calculate present value of the bond

To calculate the price of the bond today (which is the present value), the future value should be discounted using the interest rate. Using the formula for present value (PV = FV / (1 + r)^[n]), where 'r' is the interest rate and 'n' is the number of periods (or years), the PV works out as \(PV = 1050 / (1 + 0.05)^1 = 1000\)
03

Calculate capital gain or loss

To calculate the capital gain or loss, the PV of the bond is compared with the initial investment. The capital gain or loss is the difference between the present value (selling price) and the price paid for the bond one year ago. Therefore, capital gain (or loss) = selling price - purchase price = \(1000 - 900 = 100\)

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