Difference in Present Value of Annuity vs Perpetuity

James is evaluating an investment that offers him an annuity of $5,000 at the end of each year for 10 years. He believes the appropriate discount rate for this investment is 6%. Additionally, he is considering a perpetuity that pays $1,200 annually, starting next year. Assuming the same discount rate of 6%, what is the difference in present value between the annuity and the perpetuity?

To calculate the present value of the annuity, use the formula:

$$ PV_{annuity} = C imes\frac{1 - (1 + r)^{-n}}{r} $$

where:

- $PV_{annuity}$ is the present value of the annuity

- $C$ is the cash flow per period ($5,000)

- $r$ is the discount rate (0.06)

- $n$ is the number of periods (10)

The present value of a perpetuity is calculated using:

$$ PV_{perpetuity} =\frac{C}{r} $$

where:

- $PV_{perpetuity}$ is the present value of the perpetuity

- $C$ is the cash flow per period ($1,200)

- $r$ is the discount rate (0.06)