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Example:Comparing Simple & Compound Interest

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Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or, money earned by deposited funds. When money is borrowed, interest is typically paid to the lender as a percentage of the principal, the amount owed. The percentage of the principal that is paid as a fee over a certain period of time (typically one month or year), is called the interest rate.


Simple interest


Simple interest is calculated only on the principal amount, or on that portion of the principal amount that remains unpaid.

The amount of simple interest is calculated according to the following formula:

where r is the period interest rate (I/m), B0 the initial balance and m the number of time periods elapsed.

To calculate the period interest rate r, one divides the interest rate I by the number of periods m.

For example, imagine that a credit card holder has an outstanding balance of \($\)2500 and that the simple interest rate is 12.99% per annum. The interest added at the end of 3 months would be,

and he would have to pay \($\)2581.19 to pay off the balance at this point.

If instead he makes interest-only payments for each of those 3 months at the period rate r, the amount of interest paid would be,

His balance at the end of 3 months would still be \($\)2500.




Compound interest


Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding. A bank account, for example, may have its interest compounded every year: in this case, an account with \($\)1000 initial principal and 20% interest per year would have a balance of \($\)1200 at the end of the first year, \($\)1440 at the end of the second year, and so on.



A formula for calculating compound interest is A = P *((1+r/n) to the power n*t)


1.  A = final amount

2.  P = principal amount (initial investment)

3.  r = annual nominal interest rate (as a decimal)

     (it should not be in percentage)

4.  n = number of times the interest is compounded per year

5.  t = number of years

Example usage: An amount of \($\)1500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. Find the balance after 6 years.

A. Using the formula above, with P = 1500, r = 4.3/100 = 0.043, n = 4, and t = 6:

So, the balance after 6 years is approximately \($\)1,938.84.




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.