You have just bought a 10-year security that pays $500 every six months. Another equally risky security also has a maturity of 10 years, and pays 10%, compounded monthly (that is, the nominal rate is 10%). What price should you have paid for the security that you just purchased

PV = $6,178.61

Explanation:

Giving the following information:

Number of years = 10

Cash flow = 500 semiannually

Discount rate = 10% compounded monthly

First, we need to calculate the semiannual interest rate:

i = 0.10/12 = 0.00833

i = (1.00833^6) - 1 = 0.051

Now, we need to calculate the final value of security:

FV = {A*[ (1+i) ^n-1]}/i

A = cash flow

FV = {500*[ (1.051^20) - 1] / 0.051

FV = $16,708.79

Finally, the present value:

PV = FV / (1+i) ^n

PV = 16,708.79/1.051^20

PV = $6,178.61