SOLUTION: This problem is stumping me. I have tried to figure out how they come up with the answer with no luck. Any help is greatly appreciated. Find the amount that results from the gi

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Question 235053: This problem is stumping me. I have tried to figure out how they come up with the answer with no luck. Any help is greatly appreciated.
Find the amount that results from the given investment.
$10 invested at 10% compounded continously after a period of 2 years. Round to the nearest cent.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
Continuous Compounding is a special formula.

The formula can be found here !!!!!

The formula is FV = PA*e^rt

e is the scientific constant 2.718281828

FV is the future value of the Amount.

PA is the present amount.

r is the interest rate per year.

t is the amount of time in years.

For your problem:

PA = $10.00
i = 10% per year.
t = 2

Formula give you:

FV = 10*e^(.1*2) = $12.21402758 which equals $12.21 to the nearest cent.

The closest you can get to continuous compounding without an excessive amount of effort is daily compounding.

The normal Future Value formula is:

FV = PA * (1+i)^n where:

FV = Future Value
PA = Present Amount
i = interest rate per time period
n = number of time periods.

For a 2 year loan, daily compounding would be calculated as follows:

i = 10% per year divided by 365 = .02739726% per day.

That winds up being a daily interest RATE of .0002739726

The number of timer periods equas the number of years * 365 = 2 * 365 = 730

Plug that into the formula and you get:

FV = 10 * (1.0002739726)^730 = $12.213693 which becomes $12.21

Continuous compounding got 12.21402 while daily compounding got 12.21369. That's a pretty close estimate.

Hourly would get even closer, but daily was ok for a reasonable estimate.