Question 204145: Please help me solve this problem.
A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account ballance is $11,445. What is the annual interest rate?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you need to find the interest rate which is a big pain in the butt if you don't have a calculator, but there are calculators out there that do that, like the texas instruments business analyst. there may even be online calculators that will do the job for you as well.
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what they are talking about, i believe, is the internal rate of return (IROR).
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the internal rate of return is the rate at which the present value of the cash flows is equal to 0.
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the present value of the cash flows is equal to 0 when the present value of the cash inflows is equal to the present value of the cash outflows.
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the present value of cash flows is usually taken to time point 0 unless otherwise indicated.
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your time periods are in years.
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the time points in your study will be:
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time point 0 = beginning of first year and start of study
time point 1 = end of first year and beginning of second year
time point 2 = end of second year and end of study.
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your cash flows will be placed at the following time points
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time point 0: -$8,000.00
time point 1: -$2,500.00
time point 2: +11,445.00
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The present worth of your cash outflows will be:
(8000) + (2500)/(1+i)
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the present worth of your cash inflows will be:
(11445)/(1+i)^2
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in order to find the rate of return without a calculator you have to pick two interest rates to start and iterate back and forth until you narrow the selection down to the interest rate at which the present value of cash flows equals 0.
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if you're lucky, you can use a calculator that will do all that iterating back and forth for you and give you the answer you want without any trouble on your part.
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i believe microsoft excel has a formula to find IROR (internal rate of return).
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an online internal rate of return calculator on the web was found at this website.
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http://www.datadynamica.com/irr.asp
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using it, i found the internal rate of return at 5%.
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to check if this is true, i did a present value of cash flows at the interest rate of 5% to see if they equal to zero indicating the rate of return used was accurate.
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- 8000 - 2500/(1.05) = -8000 - 2380.952381 = - 10380.95238
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+ 11445 / (1.05)^2 = + 10380.95238
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since the present worth of cash flows = present worth of cash inflows minus present worth of cash outflows = 0%, this means that 5% is the internal rate of return of the investment.
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the main thing you had to worry about is setting up the problem correctly.
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$8000 was invested at time point 0 which is the beginning of year 1 and the start of the study so no adjustment was required to make the present value at time point 0. it was already there.
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$2500 was invested at time point 1 which is the end of year 1 and the beginning of year 2 so it had to be brought back 1 time point to make the present value at time point 0.
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$11445 was received at time point 2 which is the end of year 2 and the end of the study so it had to be brought back 2 time points to make the present value at time point 0
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