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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

Respuesta :

ajeigbeibraheem

Answer:

PV = $733,271

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;

[tex]PV = \dfrac{P}{r-g}\Big ( 1 - \Big ( \dfrac{1+g}{1+r} \Big) ^n \Big)[/tex]

[tex]PV = \dfrac{50000}{0.05-0.02}\Big ( 1 - \Big ( \dfrac{1+0.02}{1+0.05} \Big) ^{20} \Big)[/tex]

[tex]PV = \dfrac{50000}{0.03}\Big ( 1 - \Big ( \dfrac{1.02}{1.05} \Big) ^{20} \Big)[/tex]

[tex]PV =1666666.667 \Big ( 1 - \Big ( 0.9714285714 \Big) ^{20} \Big)[/tex]

[tex]PV =1666666.667 \Big ( 1 -0.5600379453 \Big)[/tex]

[tex]PV =1666666.667 \Big (0.4399620547 \Big)[/tex]

[tex]PV =\$733270.0913 \\ \\ \mathbf{PV \simeq \$733,271}[/tex]

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