Question 1114286: If a firm invests amount P0(0 is subscript) at an interest rate of r%, then a year later invests amount P1(1 is subscript) at the same rate, then the total amount at the end of two years is given by the formula A=P0(1+r)squared +P1(1+r).(The 0 and 1 after the Ps are subscript) A firm invests $3000, then a year later invests an additional $1700. At the end of two years, it has a total of $5173. What is the interest rate?
The interest rate is r=______%. (Round to the nearest integer.) Thank you so much!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! they invest 3000 the first year and 1700 the second year at r% per year.
at the end of the the second year, they have 5173 dollars.
what was the interest rate?
your formula is 3000 * (1 + r)^2 + 1700 * (1 + r)^1 = 5173
i don't believe there's a formula you can use to find the interest rate directly.
it is usually an iterative process that narrows it down until you get close enough to claim a solution.
you can use a calculator as long as you know what you're doing.
you can also use excel, which is a calculator in spreadsheet form, and has formulas that can help you to find the answer much less painfully than doing it by hand.
i used excel and came up with an answer of r = 0.060024814, which is equal to 6.0024814% which can be rounded to 6%.
the technique was to use the cash flow internal rate formula of excel, called IRR.
i set up the cash flow with 3000 in time point 0 and 1700 in time point 1.
these were entered as negative values.
in time point 2, i put 5173, which is the amount that is expected at the end of the 2 year period.
i then used IRR function of excel to find the internal rate of return.
the calculator gave me an internal rate of return of 0.060024814.
this is the rate, not the percent.
multiply that by 100 and you get the percent as shown above.
you can also use excel to help you with the calculations required to find it manually through iteration.
i did that through excel and was able to narrow it down pretty closely if i claimed an answer when was within .01 units of the desired answer.
it's not usually done manually because it's a laborious process.
the quickest way is to set up the cash flow is as i described above.
it can be done through excel as i just did.
it can also be done through use of the Texas Business Instrument Business Analyst II , or any other calculator that can performed cash flow analysis and find the internal rate of return for you, by setting up a similar type of cash flow.
the trick with the cash flows, is you set up your investments as negative and then make your future value positive.
the IRR function then calculates the rate of return required to make the net present value of all the cash flows equal to 0.
looking at the cash flow in excel, you can calculate the NPV as follows:
-3000 / (1+0.060024814)^0 = -3000
-1700 / (1+0.060024814)^1 = -1603.736042
5173 / (1+0.060024814)^2 = 4603.736040
sum of all present value of cash flows = -2.39140000 * 10^-6.
this is equivalent to -.0000023914 in decimal format.
round this to 5 decimal places and it becomes 0.
the difference from 0 is due to internal rounding done by the calculator.
bottom line:
if you try to do it manually through iteration, you need a good iteration routine and you will still have lots of calculations to go through.
if you set up your cash flow correctly, you can have the calculator, or excel, do it for you with a lot less pain.
my excel spreadsheet is shown below:
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