A $50 perpetuity paid monthly has a present value of $7500 on the date of the first payment. What is the annual effective rate of interest?

A perpetuity is a type of annuity that pays out indefinitely. The present value of a perpetuity can be calculated using the formula:

PV = P / r

where: PV = present value of the perpetuity P = payment per period (in this case, $50 per month) r = interest rate per period

In this case, we know the present value (PV = $7500) and the payment (P =$50), and we want to find the interest rate (r). We can rearrange the formula to solve for r:

r = P / PV

Substituting the given values:

r = $50 /$7500 = 0.00666667 per month

This is the monthly effective interest rate. To find the annual effective interest rate, we use the formula:

i = (1 + r)^12 - 1

Substituting the value of r:

i = (1 + 0.00666667)^12 - 1 = 0.0833 or 8.33%

So, the annual effective rate of interest is 8.33%.