How do you compound something to the millisecond?
like you would use the n value = 12 for monthly, 2 for semi annually, etc
HOW ABOUT FOR MILLISECOND?
The answer hasn't changed since Bobpursley posted it for you a little while ago.
http://www.jiskha.com/display.cgi?id=1379033752
Please use the same name for your posts.
see
http://www.jiskha.com/display.cgi?id=1379033752
If you are dealing with milliseconds, your compounded becomes, for all practical purposes, "continuous compouning"
in that case you can use:
Amount = principal e^rt , where r is the annual rate in decimals
e.g. suppose we have $100 at 8% compounded monthly for 2 years
amount = 100(1.006666...)^24 = 117.2888
at 8% per annum compounded by the second for 2 years
amount = 100(1.000000152)^1051200 = 117.350222
compounded continuously at 8% per annum for 2 yrs
amount = 100 e^(2(.08)) = 117.3510871
Notice in terms of money to the nearest cent, the last two results are the same, even though I did not do the milliseconds
To compound something to the millisecond, we need to find the effective interest rate for that specific time period. The compound interest formula can be used to calculate the final amount when the principal amount is compounded over a given time period.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (including principal and interest)
P = Principal amount (initial investment)
r = Annual interest rate (expressed as a decimal)
n = Number of compounding periods per year
t = Time, in years
To compound something to the millisecond, we need to determine the equivalent values for 'r', 'n', and 't'. In this case, we want to compound for milliseconds, meaning the compounding period will be every millisecond. However, it is crucial to note that compound interest is typically used for longer-term investments, and compounding to the millisecond may not be practical or realistic in most scenarios.
To calculate the equivalent values for 'r', 'n', and 't', we need to convert the annual interest rate to a rate per millisecond and determine how many milliseconds are in a year.
1 year = 365 days × 24 hours × 60 minutes × 60 seconds × 1000 milliseconds
Let's assume the annual interest rate is 6%. Here's how you can calculate the compounding variables for milliseconds:
1. Convert the annual interest rate to a decimal:
r = 6% = 0.06
2. Calculate the rate per millisecond:
rate_per_ms = r / (365 * 24 * 60 * 60 * 1000)
3. Determine the number of compounding periods per year (n):
n = 1 / rate_per_ms
4. Set the time (t) to 1 millisecond (or any desired time period).
Now, you can substitute the calculated values of 'r', 'n', and 't' into the compound interest formula to find the final amount after compounding to the millisecond.
It's important to mention that while the above process demonstrates how to calculate compounding to the millisecond, it may not be practically applicable due to various factors, including system limitations and the nature of compounding interest for shorter time periods.