Question 248957: I need someone to tell me where "m" come from?
If $1,000 is invested in an account paying 10% compounded monthly, how much will be in the account at the end of 10years? compute the answer to the nearist cent.
Compound interest formula:
A=P(1+(r/m))^(mt)
P=1,000
r=0.1
m=12
t=10
A=1,000(1+(0.10/12)^((12)(10))
A=$2,707.04
Found 2 solutions by kensson, Theo:
Answer by kensson(21)   (Show Source):
You can put this solution on YOUR website! The m is the number of periods the year is split into - here, it's 12 because the interest is compounded monthly. If it was daily, m would be 365.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! m looks like it is months.
usually you are given the annual interest rate and you have to divide that by the number of months to get the monthly interest rate.
this assumed the compounding of the interest rate is monthly.
It could be:
semi-annually (2)
quarterly (4)
monthly (12)
yours is monthly.
if the compounding is monthly, then the number of time periods have to be in months.
if they are specified in years, then you have to multiply them by 12 to get months.
your formula is:
If $1,000 is invested in an account paying 10% compounded monthly, how much will be in the account at the end of 10years? compute the answer to the nearist cent.
Compound interest formula:
A=P(1+(r/m))^(mt)
P=1,000 ***** money invested in the account today.
r=0.1 ***** annual interest rate of 10% per year.
m=12 ***** compounding period is in months and there are 12 months to the year.
t=10 ***** number of years
A=1,000(1+(0.10/12)^((12)(10))
A=$2,707.04
you take the annual interest rate and divide it by 12 to get the monthly interest rate per time period equal to .000833333333
you take the number of years and multiply it by the number of months in a year to get the number of time periods equal to 120
your formula becomes:
A = 1,000 * (1.00833333^120)
Your answer of 2707... is correct.
A more general formula would be:
F = P * (1+(r/c)^(n*c)) where:
F = future value
P = present amount
r = annual interest rate
c = number of compounding periods per year
n = number of years
this works with all compounding periods, not just months.
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