Your grandfather left you an inheritance that will provide an annual income for the next 10 years.You will receive the first payment one year from now in the amount of $3,000.Every year after that,the payment amount will increase by 6 percent.What is your inheritance worth to you today if you can earn 9.5 percent on your investments?

Question

Quizplus · Accepted Answer

This is a problem involving the calculation of the present value of a growing annuity. The formula to calculate the present value of a growing annuity is: $PV = \frac{C}{r-g} \times \left(1 - \left(\frac{1 + g}{1 + r}\right)^t\right)$, where $PV$ is the present value of the annuity, $C$ is the initial payment, $r$ is the discount rate, $g$ is the growth rate of the annuity, and $t$ is the number of periods. Plugging in the given values: $C = \$3,000$, $r = 9.5\% = 0.095$, $g = 6\% = 0.06$, and $t = 10$, we get $PV = \frac{\$3,000}{0.095 - 0.06} \times \left(1 - \left(\frac{1 + 0.06}{1 + 0.095}\right)^{10}\right)$, which calculates to approximately \$23,774.36.

Your Grandfather Left You an Inheritance That Will Provide an Annual