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A financial advisor says she has an investment that will pay you $500 a month forever....

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Finance

A financial advisor says she has an investment that will pay you$500 a month forever. It will cost you $25,000 today. Whateffective annual rate (EAR) will you earn on this investment? Roundyour answer to the nearest tenth of a percent.

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Information provided:

Monthly payment= $500

Present value of the perpetuity= $25,000

Present value of the perpetuity payment= annual payment/ Interest rate

$25,000= $500/ Interest rate

Interest rate= $500/ $25,000

                        = 0.02*100

                        = 2% per month

Annual interest rate= 2%*12= 24%

Effective annual rate is calculated using the below formula:

EAR= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

EAR= (1 + 0.24/12)^12 – 1

        = 1.2682 -1

        = 0.2682*100

        = 26.82%

Therefore, the Effective annual rate on the investment is 26.8%.

In case of any query, kindly comment on the solution.
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Transcribed Image Text

A financial advisor says she has an investment that will pay you$500 a month forever. It will cost you $25,000 today. Whateffective annual rate (EAR) will you earn on this investment? Roundyour answer to the nearest tenth of a percent.

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