Question

A growing perpetuity is currently valued $6,225.81. The next annuity payment will be $386 and the discount rate is 9 percent. What is the annuity's rate of growth

Answer 1

To find the annuity's rate of growth, use the formula g = r - PMT / PV with the given values: 0.09 for the discount rate (r), $386 for the payment (PMT), and $6,225.81 for the present value (PV).

Step-by-step explanation:

The question asks how to determine the annuity's rate of growth for a growing perpetuity valued at $6,225.81 with the next annuity payment being $386 and a discount rate of 9 percent. The value of a growing perpetuity can be calculated using the formula:

Present Value (PV) = Payment (PMT) / (Discount Rate (r) - Growth Rate (g))

We can rearrange the formula to solve for the growth rate (g) since we have the present value, the payment, and the discount rate:

g = r - PMT / PV

Plugging in the given values:

g = 0.09 - 386 / 6,225.81

Doing the calculations provides the annuity's rate of growth.

Answer 2

2.8%

Step-by-step explanation:

The formula to calculate value of a perpetuity is as follow:

V = Annuity payment in year 1 / (r-g)

V: Value of the perpetuity

r: Discount rate

g: Growth rate (missing value)

By inputting numbers into the formula, we have:

6225.81 = 386 / (0.09 - g)

--> g = 2.8%