Question

You have just bought a security that pays $500 every six months. The security lasts for 10 years. Another security of equal risk also has a maturity of 10 years, and pays 10 percent compounded monthly (that is, the nominal rate is 10 percent). What should be the price of the security that you just purchased?.

Answer 1

PV= $6,178.61

Step-by-step 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