The Compound Interest Equation
First to calculate Compound Interest we have to know what it is. You can read here below a shorten explanation or you can click here for a full explanation.
What is Compound Interest
Compound interest simply means to earn interest on interest. If you're to start off with 100 dollars and receive an interest of 10 percent per month, after the 1st month you would have $110, after the 2nd month you would have $121, after the 3rd month you would have $133.10. As you could see, your money increases at an accelerating rate as you earn interest on interest; that is what is meant by the power of compound interest. Compound interest is the interest charged on any unpaid interest. This is the most expensive type of interest of all. Commercial lenders charge this type of interest. The following example explains how to use compound interest formula to calculate the total cost of borrowing if interest is calculated as compound interest.
The Compound Interest Equation
P = C (1 + r/n) nt
where
P = future value
C = initial deposit
r = interest rate (expressed as a fraction: eg. 0.06)
n = is how much year interest is compounded
t = number of years invested
Simplified Compound Interest Equation
When interest is only compounded 1 time per year (n=1), the equation simplifies to:
P = C (1 + r) t
Continuous Compound Interest
When interest is compounded continually (i.e. n --> ), the compound interest equation takes the form:
P = C e rt
Demonstration of Various Compounding
The following table shows the final principal (P), after t = one year, of an account initially with C = $25000, at 7% interest rate, with the given compounding (n). As is shown, the method of compounding has little effect.
Loan Balance
Situation: A person initially borrows an amount A and in return agrees to make n times repayments per year, each of an amount P. While the person is repaying the loan, interest is accumulating at an annual percentage rate of r, and this interest is compounded n times a year (along with each payment). Therefore, the person must continue paying these installments of amount P until the original amount and any accumulated interest is repaid. This equation gives the amount B that the person still needs to repay after t years.
B = A (1 + r/n)NT - P (1 + r/n)NT - 1
(1 + r/n) - 1
where
B = balance after t years
A = amount borrowed
n = number of payments per year
P = amount paid per payment
r = annual percentage rate (APR)
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