For an investment of $20,000 today at j₂ = 4%,you expect to receive three payments of $R,one each at the end of 1,2 and 3 years.If the probability of default for any payment is 3%,what should the value of R be? A)$7083.22 B)$7435.51 C)$7656.95 D)$8123.83

Question

Quizplus · Accepted Answer

Using the formula for present value of an annuity,

PV=R*(1-(1/(1+0.04)^3))/0.04

Also, the expected value of each payment is (1-0.03)*R=R*0.97

Therefore, the expected present value of all payments is

E(PV)=3*(R*0.97)*(1-(1-0.03)^3)/(0.04*(1+0.03)^3)

This expected present value should be equal to the initial investment of $20,000.

20,000=E(PV)

20,000=3*(R*0.97)*(1-(1-0.03)^3)/(0.04*(1+0.03)^3)

Solving for R, we get R=$7656.95. Therefore, the correct choice is C.

For an Investment of $20,000 Today at J2 = 4%,you

For an Investment of $20,000 Today at J₂ = 4%,you