Question

An investment pays $1500 every three years with the first payment starting one year from now (i.e., second payment is on t=4). If “effective two year” rate on this project is 10%, estimate the present value of the investment.

A. $9,151

B. $9,350

C. $9,766

D. $10,742

Answer 1

     

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We wil calculate the APR Rate as effecitve rate for 2 years is given and we need Effective rate for 3 years. First we calculate the APR and then make it effective for 3 years.

EAR = ((1+APR)^(2)) - 1

0.10 = ((1+APR)^(2)) - 1

1.10^(1/2) = (1+APR)

APR = (1.04880884817 -1)

APR = 4.88%

Effective Rate for 3 years = ((1 + 0.0488) ^3) -1

= 1.15366053427 - 1

= 15.37%

We will calclate the present value on years end 1 and then discount the value to present in the next step.

Present Value of annuity after one year = 1500 + 1500 / 0.1537

= 11259.2713077

Present Value today = 11259.2713077 / (1.0488)

= 10,742

Option D is correct.