Compound Interest

When you borrow money from a bank, you pay interest. Interest is really a fee charged for borrowing the money, it is a percentage charged on the principle amount for a period of a year - usually.

If you want to know how much interest you will earn on your investment or if you want to know how much you will pay above the cost of the principal amount on a loan or mortgage, you will need to understand how compound interest works.

* Compound interest is paid on the original principal and on the accumulated past interest.

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Conversion periods are:

Semi-Annually = (m = 2)

Annually = m = 1 / P × (1 + r) = (annual compounding)

Quarterly = m = 4 / P (1 + r/4)4 = (quarterly compounding)

Monthly = m = 12 / P (1 + r/12)12 = (monthly compounding)

The fundamental formula for compound amount is: F = P(1 + i)n

F = compound amount

P = original principal i = interest per conversion period which is equal to nominal rate (j) divided by the conversion period (m) n = total number of conversions period for the whole term; (m * t)

Illustrative Examples:

1.) Find the compound interest on P1,000 at the end of 8 ½ years at 8% compounded quarterly.

P = P1,000 j = 8% m = 4 (quarterly) t = 8 ½ years i = 8%/3 = 2% = .02 n = 34 interest periods

F = P(1 + i)n

F = 1,000 (1 + .02)34 = 1,000 (1.960676) = P1,960.68 --> compound amount { By Scientific Calculator: Press 1.02, xy , 34, =, x, 1000, = }

P1,960.68 – 1,000 = P960.68 -> compound interest

2.) Accumulate P5,000 for 25 years at 9% compounded monthly.

P = P5,000 i = 9/12 = 3/4% = 7.5% = .0075 j = 9% t = 25 years m = 12 (monthly) n = 25 x 12 = 300

F = 5,000 (1 + .0075)300 = P5000 (1 +

References: Malaborbor, Pastor B. et al. Mathematics of Investment by Scientific Calculator. Mandaluyong City: National Book Store, 2006 http://math.about.com/library/weekly/aa042002a.htm. Deb Russel. http://www.epubbud.com/read.php?g=9K7ZE5WZ&p=5