Question

Rhoda Morgenstern just settled an insurance claim. The settlement calls for increasing payments over a 20-year period. The first payment will be paid one year from now in the amount of $50,000. The following payments will increase by 2 percent annually. What is the value of this settlement to Rhoda today if she can earn 5 percent on her investments

Answer 1

PV = $733,271

Step-by-step explanation:

From the given information:

The annual payment (P) = $50,000

number of years (n) = 20

The growth percentage = 2% = 0.02

Rate of percentage earned = 5% = 0.05

Using the formula illustrated below to determine the Present Value (PV) of a growing annuity;

`PV = (P)/(r-g)\Big ( 1 - \Big ( (1+g)/(1+r) \Big) ^n \Big)`

`PV = (50000)/(0.05-0.02)\Big ( 1 - \Big ( (1+0.02)/(1+0.05) \Big) ^(20) \Big)`

`PV = (50000)/(0.03)\Big ( 1 - \Big ( (1.02)/(1.05) \Big) ^(20) \Big)`

`PV =1666666.667 \Big ( 1 - \Big ( 0.9714285714 \Big) ^(20) \Big)`

`PV =1666666.667 \Big ( 1 -0.5600379453 \Big)`

`PV =1666666.667 \Big (0.4399620547 \Big)`

`PV =\$733270.0913 \\ \\ \mathbf{PV \simeq \$733,271}`