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.
