SOLUTION: I need help with this question. An intial investment of $5000 earns 8% interst, compounded continuously. What will the investment be worth in 15 years?

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Question 128843: I need help with this question.
An intial investment of $5000 earns 8% interst, compounded continuously. What will the investment be worth in 15 years?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
For continuous compounding remember PERT.

A+=+Pe%5E%28rt%29, where P is the original principal, r is the rate per time period, and t is the number of time periods. You have an annual rate and a number of years - that matches, so just use the numbers, remembering to convert 8% to a decimal fraction (0.08). And e is the base of the natural logarithms, approx 2.718...

A=5000%2Ae%5E%28.08%2A15%29

Using the Windows calculator in scientific mode:
0.08 * 15 = 1.2
Check the INV box, then press the "ln" button, then * 5000 = 16600.58
This works because the inverse (INV box checked) of the natural log (ln) is e%5Ex

This answer also makes sense because using the rule of 72, we know that an 8% investment should double every 9 years (actually a little faster than that with continuous compounding), so having the money more than triple in 15 years is reasonable.