Let me ask each of you a question . . . would you rather have $1000 today (Optio
ID: 2663957 • Letter: L
Question
Let me ask each of you a question . . . would you rather have $1000 today (Option A), or $100 today and at the first of each year for eleven years (Option B)? The answer seems pretty straightforward - $1100 is better than $1000. But TVM takes into account the value of interest earned (or sacrificed) depending when the funds are received. The future $100 dollar payments will each be worth slightly less than that in today's dollars depending on the interest rate. There is a breaking point where option A is best, or option B becomes best, depending on the rate. So, what is that rate?Explanation / Answer
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Ok to do this we need to take the future value of $1000 and set it equal to the present value of a $100 annuity as such:
FV = FV(A)
PV * (1 + i)n = A * [(1+i)11-1]/i
$1000 * (1 + i)11 = $100 * ((1+i)11-1)/i
Now we need to get the i by itself, which clearly is going to be a challenge. Therefore I'm simply going to plug in varying values of i until they are equal (NOTE: you can also use the future value tables for an annuty and a single amount)
Starting with 1% interest:
1000 * 1.1157 = 1115.7
100 * 11.5668 = 1156.7
We can see that these are very close, but the annuity is better. If you do it with 2% interest you will get the single amount being better. Therefore, the interest rate must be somewhere between 1% and 2%. I did a list in my graphing calculator to do the same calculation for varying inputs of i and I found that they are equal when i = 0.0165 or 1.65%. I am assuming you have taken a statistics class because it's usually a prereq for finance, but if you haven't learned how to use lists on a graphing calculator then just google it or you'll just have to keep pluging in numbers.
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