An American that puts away their money to earn interest until they need to count on the dollar and cents on a later day can earn much more than flat interest will earn for them. Putting compound interest in the financial plan will give them financial security and a growing yield.

They just have to know exactly how their money money growth this year always outdoes last year's growth.

The Principal

The ins and outs of compound interest begin with the money that goes into the account the first day, the principal. The greater the amount that goes in, the more the money will earn. A year is enough time for the principal to grow.

P = P0 + (P0*r) is the standard formula for a principal that earns interest. Yield is highest on the largest original principal, P0. The principal today, P, got its size from the P0 and growth in interest, r, in the fullness of time.

The amount is easy to calculate.

For example, an investor invests $100 the first day in their savings account that earns 1 percent annual interest. At the end of the year, when they look at their balance, the amount in the account is 100 * (100*.01) = $101.

Investments

Making another investment in the account adds to the bottom line, and the change the account earns in return. Nothing stops an investor from raising the principal amount. An investment is the start for another principal amount that adds to the first and all other investments before it. The investor can watch an investment, I0, grow from the first day just like they watch the principal.

The formula I = I0 + (I0*r) tells the investor how the investment principal earns interest. Adding P and I together produces the full amount for today with the total interest earned on the principal amounts.

Investing another $10 in the account raises the invested money balance to $110. After the $10 is in the account 1 year, the investment amount grows to $10.10.

Interest

Returns are earned in dollars and cents that depend on the rate of interest. The return earned on the investment is called interest, INT. In other words, the interest is an investor's share of the gains made on the money the investor handed over to a money manager that invests the money in productive enterprises.

The longer an investor waits to use their money the higher the result of the formula INT = money*(r*number of years) will be. The most simple formula is INT = money*r used when the money is in the account for 1 year. It can substitute for P0*r in the principal formula and I0*r in the investment formula.

Rates of interest, r, range from 1 percent on a savings account to 4 percent on a money market account to 8 percent on a diverse 401(k) portfolio with growth stocks. The money till grows much faster with a high r.

The interest earned on any 1 dollar put into a savings account that earns 1 percent interest after one year is 1 * .01 = 1 cent.

Interest on Principal and Investments

Money starts to grow the first day in the account that earns compound interest. As long as the money is not taken out, the amounts will earn interest that compounds as often as the account manager has agreed, e.g. annually, quarterly, monthly, or daily. At the end of each period, the interest will be in the account added to the principal that was in the account at the beginning of the period.

INT = P*r.

The same is true of interest on the amount invested after the original principal. After a length of time, the interest on the investment will be in the account.

INT = I*r.

The interest earned on the $100 principal after 1 year is 100*.01 = 1 dollar.

The interest earned on the $10 investment after 1 year is 10*.01 = 10 cents.

Interest on Interest

Compound interest always grows like a mushroom. The interest on interest, IOI, produces special growth. Interest money begins to earn interest as soon as the account manage puts the earned money in the account and adds it to the principal.

IOI = INT0*r. At the end of any period, the IOI is the part of the interest that is in the P that was earned on interest, not on the principal or an investment. All interest bearing accounts earn interest on the principal and investments. Only the compound interest accounts earn the IOI.

During the second year the $100 is in the account, the interest on the $1 earned in interest the first year is 1*.01 = 1 cent.

The 10 cents interest earned on the $10 investment, during the second year the $10 is in the account, earns interest in the amount of one-tenth of a penny.

Lasting Interest

Constantly increasing growth never wears out. Interest will add to the balance during every investment period.

U. S. Labor Department, Savings Fitness: A Guide To Your Money and Your Financial Future (October 2010).