Your grandfather left you an inheritance that will provide an annual income for the next 20 years. You will receive the first payment one year from now in the amount of $2,500. Every year after that, the payment amount will increase by 5 percent. What is your inheritance worth to you today if you can earn 7.5 percent on your investments?

Question

Quizplus · Accepted Answer

To find the present value of the inheritance, we need to discount the future cash flows back to present using the given discount rate of 7.5%.

We can use the formula for the present value of an annuity with growth:

PV = C / (r-g) * (1 - (1+g)/(1+r)^n)

where 
C = first payment = $2,500 
r = discount rate = 7.5% or 0.075 
g = growth rate = 5% or 0.05 
n = number of years = 20

Plugging in the values, we get:

PV = 2500 / (0.075 - 0.05) * (1 - (1+0.05)/(1+0.075)^20) 
PV = $37,537.88

Therefore, choice A is the correct answer as it represents the present value of the inheritance.

Your Grandfather Left You an Inheritance That Will Provide an Annual