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 Compound Interest Consumer Mathematics with FREE Online Calculator

Compound interest is when interest is calculated on principal and any previously earned interest.

Let's consider an example.  You invest \$500 at a 5% annual interest rate.   After the first year, the account would earn interest of:

I = Prt = 500 * .05 * 1 = \$25

If you re-invest this \$25 in earned interest, then at the beginning of the 2nd year, the account would have \$525 as principal.  During the 2nd year, the account would earn interest of:

I = Prt = 525 * .05 * 1 = \$26.25

which is \$1.25 more than what was earned in the first year.  Compound interest has the property that earned interest is automatically reinvested to earn additional interest.

The formula for calculating the accumulated value via compound interest is as follows:

A = P(1 + r/m)n

where A is the accumulated value, P is Principal, r is the annual interest rate, m is compounding frequency, and n is the total number of periods.

Example 1  Calculate the interest earned from a \$4,500 loan compounded quarterly at 5% for 6 years.

Here, P = \$4,500, r = 5% = .05, and m = 4 (quarterly).  Over 6-years, there are n = 4*6 = 24 quarters.  The accumulated value is:

A = (4500)[1 + .05/4]24 = 6063.08

I = A - P = 6063.08 - 4500 = 1563.08

Example 2  A savings account pays 4% interest and is compounded daily (365 days).  When will the accumulated value be twice the original principal?

We are solving for n:

2P = P( 1 + .04/365 )n

log 2 = n log (1 + .04/365)

n = log 2 / log (1 + .04/365) = 6325.32

n is the number of periods which for this example, is in days.  It will take 6325 days to double the principal, which is roughly 6325/365 = 17.32 years.

The online calculator below calculates simple interest.

 Change the loan amount to the right and then click Calculate.

Compound Interest
 Principal \$ Annual Interest Rate % Time (in years)
 Interest earned Accumulated Value \$