Question 235053
Continuous Compounding is a special formula.


The formula can be found <a href = "http://cs.selu.edu/~rbyrd/math/continuous/" target = "_blank">here !!!!!</a>


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.