Final answer:
To find the present value of a perpetuity growing at 5% annually with a 7% interest rate, you would use the formula PV = P / (r - g). Plugging the given values into this formula yields a present value of $5,000, indicating that none of the provided options are correct.
Step-by-step explanation:
The question asks to calculate the present value of a perpetuity that pays $100 every year, which grows at 5% annually, given a 7% annual interest rate. This is solved using the formula for the present value of a growing perpetuity:
PV = P / (r - g)
Where PV is the present value, P is the first payment, r is the interest rate, and g is the growth rate of the payment.
When we plug in the given values:
P = $100
r = 7% or 0.07
g = 5% or 0.05
The present value is calculated as:
PV = $100 / (0.07 - 0.05)
PV = $100 / 0.02
PV = $5,000
In this case, none of the provided options (a. $1,429 b. $1,571 c. $2,000 d. $2,857) are correct. You would pay $5,000 to receive $100 every year, growing at 5%, annually, forever.