How long would it take $1,000 to double if it were invested in a bank that pays 6 percent per year? How long would it take if the rate were 10 percent?

We sometimes need to know how long it will take to accumulate a given sum of
money, given our beginning funds and the rate we will earn on those funds. For example, suppose we believe that we could retire comfortably if we had $1 million, and we want to find how long it will take us to have $1 million, assuming we now have $500,000 invested at 4.5 percent. We cannot use a simple formula the situation is like that with interest rates. We could set up a formula that uses logarithms, but calculators and spreadsheets can find N very quickly. Here’s the calculator setup:
Enter I/YR
4.5, PV
500000, PMT
0, and FV
1000000. Then, when we press the N key, we get the answer, 15.7473 years. If you plug N
15.7473 into the FV formula, you can prove that this is indeed the correct number of years:
FV
PV(1  I)N
$500,000(1.045)15.7473
$1,000,000 We would also get N
15.7473 with a spreadsheet.
How long would it take $1,000 to double if it were invested in a bank that pays 6 percent per year? How long would it take if the rate were 10 percent?
Microsoft’s 2004 earnings per share were $1.04, and its growth rate during the prior 10 years was 24.1 percent per year. If that growth rate were maintained, how long would it take for Microsoft’s EPS to double?

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