You invest $50,000 now and receive $10,000 per year for 15 years starting at the end of the first year. What is the payback period in whole number years for this investment? In other words, in what year do you break even on this investment? Use i = 9% annual rate compounded annually, and use the discounted payback approach (not Simple Payback)

Question

Mathews

Business

8 November, 17:22

You invest $50,000 now and receive $10,000 per year for 15 years starting at the end of the first year. What is the payback period in whole number years for this investment? In other words, in what year do you break even on this investment? Use i = 9% annual rate compounded annually, and use the discounted payback approach (not Simple Payback)

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Answers (1)

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Lilianna Austin · Answer 1

Number of years = 7.064 years

Explanation:

Giving the following information:

You invest $50,000 now and receive $10,000 per year for 15 years starting at the end of the first year. I = 9%

Io = 50,000

I1 = 10,000/1.09 = 9,174.31

Collected payback = 9174.31

I2 = 10000/1.09^2 = 8416.80

Collected payback = 17,591.11

I3 = 10000/1.09^3 = 7721.83

Collected payback = 25,312.94

I4 = 10000/1.09^4 = 7,084.25

Collected payback = 32,397.19

I5 = 10000/1.09^5 = 6,499.31

Collected payback = 38,896.5

I6 = 10000/1.09^6 = 5,962.70

Collected payback = 44,859.2

I7 = 10000/1.09^7 = 5470.34

Collected payback = 50,329.54

Number of years = 7 years + [329.54 / (50000-44859.2) ] = 7.064 years