Can you do an example for the total amount given an principal of $12,000?

Question

Exponential functions are used to calculate continuously compounding interest rates.

For example, pretend a bank is offering 12% interest, compounding annually.

You would make 12% that year.

If it is compounding monthly, you'd make effectively 1.01^12 = 12.68%

If it is compounding daily, you'd make effectively 1.000328^365 = 12.747%

If you've had calculus, you know about infinite series. If you break the compounding periods down into infinity, to where it is "continuously compounding", it converges to e^r*t. So in our above example, e^.12 = 12.7497%.

This concept is used in a lot of financial markets for asset pricing, etc.

e is also used a lot in statistics.

Answer 1

$12,000 at 12.00% = $1,400 interest
$12,000 at 12.68% = $1,521.90 interest
$12,000 at 12.747% = $1,529.70 interest
$12,000 at 12.7497% = $1,529.96 interest

Just add $12,000 to each amount, to get the total.

Answer 2

A =12,000* e^rt where r =0.12 example and t in years
formula for continuos compounding
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