The value of a perpetuity of $100 growing at 3% per year with an 8% discount rate is:

To determine the value of a perpetuity, particularly one that grows over time, we can use the formula for the present value of a growing perpetuity:

[ PV = \frac{C}{r - g} ]

Where:

• ( PV ) is the present value of the perpetuity,

• ( C ) is the cash flow per period ($100 in this case),

• ( r ) is the discount rate (8% or 0.08), and

• ( g ) is the growth rate (3% or 0.03).

Plugging the numbers into the formula:

[ PV = \frac{100}{0.08 - 0.03} ]

Calculating the denominator:

[ 0.08 - 0.03 = 0.05 ]

Now substituting this back into the formula:

[ PV = \frac{100}{0.05} = 2000 ]

This calculation shows that the present value of a perpetuity of $100, growing at 3% per year with an 8% discount rate, is indeed $2,000. This is why the correct answer is identified as B.

The approach effectively captures the value of future cash