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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

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facundobuzzetti

Answer:

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

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