Question

A)What is the present value of a security that will pay $47,000 in 20 years if securities of equal risk pay 8% annually? Do not round intermediate calculations. Round your answer to the nearest cent.

B)Your parents will retire in 28 years. They currently have $210,000 saved, and they think they will need $1,300,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

C)What is the present value of a security that will pay $47,000 in 20 years if securities of equal risk pay 8% annually? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

A. The present value is computed as shown below:

Present value = Future value / (1 + r )ⁿ

= $ 47,000 / ( 1 + 0.08 )²⁰

= $ 10,083.77 Approximately

B. The annual rate of interest is computed as follows:

Future value = Present value ( 1 + r )ⁿ

$ 1,300,000 = $ 210,000 ( 1 + r )²⁸

( $ 1,300,000 / $ 210,000 )^{1 / 28} - 1 = r

r = 6.73% Approximately

C. The present value is computed as shown below:

Present value = Future value / (1 + r )ⁿ

= $ 47,000 / ( 1 + 0.08 )²⁰

= $ 10,083.77 Approximately

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