Question

A perpetuity pays $5,000 per year, with the first payment coming one year from now. If the appropriate annual interest rate is 6%, what is the perpetuity's present value?

a. $78,408.33
b. $83,333.33
c. $88,333.33
d. $85,833.33
e. $80,833.33

Answer 1

The present value of a perpetuity that pays $5,000 per year with a 6% annual interest rate is $83,333.33.

Step-by-step explanation:

The present value of a perpetuity can be calculated using the formula PV = PMT / r, where PV is the present value, PMT is the payment per period, and r is the interest rate per period.

In this case, the perpetuity pays $5,000 per year, and the annual interest rate is 6%, which we express as 0.06 in decimal form. Plugging these values into the formula gives us:

PV = $5,000 / 0.06

So the present value of the perpetuity is:

PV = $5,000 / 0.06 = $83,333.33

The correct answer to the student's question is b. $83,333.33.

To find the present value of the perpetuity, we can use the formula: PV = Payment / Interest Rate

In this case, the payment is $5000 per year and the interest rate is 6%.

Substituting these values into the formula, we have:

PV = $5000 / 0.06 = $83,333.33

Therefore, the present value of the perpetuity is $83,333.33. So, the answer is b. $83,333.33.