Question 541121
Sure. You're looking for the compounding formula:
{{{p*((1+i)^n)=x}}}
"P" is the principal amount
"i" is the interest rate in each compounding period
"n" is the number of compounding periods
and you're solving for "x" - the new amount of money.
To figure out the interest rate per compounding period, take the simple rate and divide by the number of periods. However for your first few problems, the period is a year, so there's no need to adjust. Simply plug your numbers into the formula.
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To find the effective rate, simply solve the equation using a principal amount of $1 over 1 year. For example, I'll work the 12% problem to show you how it's done:
{{{p*((1+i)^n)=x}}}
Using:
P=1
i=12% / 12=1%=.01
n=1year*12months=12 periods
{{{p*((1+i)^n)=x}}} becomes
{{{1*((1+.01)^12)=x}}}
{{{((1.01)^12)=x}}}
{{{x=((1.01)^12)=1.1268}}}
Meaning an increase of 12.68%