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.The probability of default of the first payment is 3%,while the probability of default of the 2^nd or 3^rd payment,given that the previous payments were made,is 3%.What should the value of R be? A)$6996.07 B)$7212.44 C)$7429.87 D)$7435.51

Question

Quizplus · Accepted Answer

To find the value of R, we need to use the present value formula for multiple cash flows with different probabilities of default:
PV = R/(1+0.04)^1 + R/(1+0.04)^2 + R/(1+0.04)^3
PV = R(1/1.04 + 1/1.04^2 + 1/1.04^3)
PV = R(2.783185)
PV = $20,000
Solving for R:
R = $20,000/2.783185
R = $7,185.511
However, we need to adjust this value for the probabilities of default. The probability that all three payments are received is (1-0.03)(1-0.03)(1-0.03) = 0.970299. Therefore, the expected value of R is:
E(R) = $7,185.511 * 0.970299
E(R) = $6,964.07
Therefore, the best choice is D, $7435.51, which is closest to the expected value of R.

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

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