Question

Your grandfather left you an inheritance that will provide an annual income for 20 years. You will receive the first payment three years 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?

Answer 1

The worth of the inheritance is $41,795.15.

The formula that can be used to determine the present value of a growing annuity is:

PV = $(\frac{A}{r - g})$ × $(1 - (\frac{1 + g}{1+r} )^{n})$

Where:

A = amount = $2500

g = growth rate = 5%

r = interest rate = 7.5%

n = number of years = 23

$(\frac{A}{r - g})$ = 2500 / 0.075 - 0.05 = 100,000

$(1 - (\frac{1 + g}{1+r} )^{n})$ = 1 - (1.05 / 1.075)^23 = 0.417951

100,000 x 0.417951 = $41,795.15

A similar question was solved here: brainly.com/question/9641711