SOLUTION: I found simple interest, I also need to find interest compounded annually and find the amount by which the compound interest is larger. $10,240 at 10% 11 years. Also $7908.42 at 5

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: I found simple interest, I also need to find interest compounded annually and find the amount by which the compound interest is larger. $10,240 at 10% 11 years. Also $7908.42 at 5      Log On

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Question 541121: I found simple interest, I also need to find interest compounded annually and find the amount by which the compound interest is larger. $10,240 at 10% 11 years. Also $7908.42 at 5% for 8 years. Also need the effective rate correspondig to the following nominal rates, then round to the nearest hundredth of a percent for 12% compounded monthly and 9% monthly. Thank you, I am basically looking for the solutions on how to do these types of problems.
Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
Sure. You're looking for the compounding formula:
p%2A%28%281%2Bi%29%5En%29=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.
.
.
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%2A%28%281%2Bi%29%5En%29=x
Using:
P=1
i=12% / 12=1%=.01
n=1year*12months=12 periods
p%2A%28%281%2Bi%29%5En%29=x becomes
1%2A%28%281%2B.01%29%5E12%29=x
%28%281.01%29%5E12%29=x
x=%28%281.01%29%5E12%29=1.1268
Meaning an increase of 12.68%