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?
Question
A 7500 on the date of the first payment. What is the annual effective rate of interest?
Solution
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 = 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 = 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%.
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