Question

A perpetuity will make payments of $100,000 every third year, with the first payment occurring three years from now. The annual nominal interest rate convertible quarterly is 8%. Find the present value of this perpetuity.

(I did this problem, just want to check if I did it correctly because the answer doesn't look right to me, not sure what I did incorrectly, I got PV = 372,800.47)

Answer 1

Your answer is pretty close. Here is the detailed solution for reference:

The nominal interest rate convertible quarterly= 8%

To arrive at the effective interest rate, we use

i= (1+(i^p)/p)^p, where p= the number of periods i.e. 4 in this case

thus, i= 8.24%

Now, since the payments are made every three years, starting three years from today, the effective interest rate every three years will be calculated as:

[(1+8.24%)^3] - 1 =0.268129 i.e 26.81%

To find the PV, simply divide the value of the perpetuity by the effective interest rate every 3 years

So,

1,00,000/.268129 = 3,72,955.148

Thus, the present value of this perpetuity is $3,72,955.148