2. (50 points) Your landlord has started a new business and proposes that you in

Question

2. (50 points) Your landlord has started a new business and proposes that you invest in it. According to him, your initial investment would be $100,000. During the first two years, you would invest an additional $20,000 per year. During the third year, the business would begin to earn a profit. He expects to return $45,000 to you in Year 3, then $50,000 in Year 4, $55,000 in Year 5, and $ 60,000 in Year 6. After year 6, you would no longer be tied to the business or receive income. He says this is equivalent to 12% interest on your investment, compounded daily. Assuming his projected payments back to you are correct, will you have made 12%, compounded annually, on your total investment? Show all your calculations to support your answer.

Explanation / Answer

R = 12%, compounding daily

Then,

Effective annual interest rate = (1+ 12%/365)^365 - 1 = 12.75%

At this rate,

Present value of all the investment = 100000 + 20000/1.1275 + 20000/1.1275^2

Present value of all the investment = $133470.8

Present value of income = 45000/1.1275^3 + 50000/1.1275^4 + 55000/1.1275^5 + 60000/1.1275^6

Present value of income = $121722.9

Since, the present value of the income at 12% is less than the present value of the cost at 12%, then it means that it is not giving me a return of 12%.The return is less than the 12%.

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