Date: 9/25/96 at 23:12:48 From: Jake Taylor Subject: math help What does the term compound interest mean? What does continuous compounding mean?
Date: 10/29/96 at 20:15:14 From: Doctor Mason Subject: Re: math help Hi Jake! Let's begin with simple interest. Simple interest is computed only once for the duration of the loan or investment. Therefore, if you plan to invest $1000 for 3 years, the bank will figure the interest only once at the end of the three years and then give it to you. Let's say the account pays 5 percent interest. At the end of three years, the bank will calculate $1000 x .05 x 3 = $150 and pay you $150 in interest. If you add that to what you started with, you will end up with $1150. Compound interest is calculated more often, and as soon as it is calculated, the interest in added to your account. That way the next time the interest is computed, you have MORE in your account than the money you put there. Let's suppose your $1000 is in an account paying 5 percent compounded semi-annually (twice a year) for three years. We can use the Simple Interest formula over and over to figure your interest. This formula is I = PRT, where I = the interest you get, P = the amount you invest, R = the interest rate written as a decimal, and T = the time in years. (For us our time is 1/2 since we're figuring the interest twice each year.): $1000.00 x .05 x (1/2) = $25 for the first 6 months. Add it to your account. $1025.00 x .05 x (1/2) = $25.63 for the second 6 months. Add it to your account. $1050.63 x .05 x (1/2) = $26.27 for the third 6 months. Add it to your account. $1076.90 x .05 x (1/2) = $26.92 for the fourth 6 months. Add it to your account. $1103.82 x .05 x (1/2) = $27.60 for the fifth 6 months. Add it to your account. $1131.42 x .05 x (1/2) = $28.29 for the last 6 months. Add it to your account. This makes for a total of $1159.71 in your account! As you can see, you end up with $9.71 more if they calculate the interest multiple times during the time the money is invested rather than just at the end. You make more money because they are paying you interest on the money they paid you earlier! Pretty neat, isn't it? The more often the interest is compounded, the more interest you earn. (By the way, banks don't do it by writing it all out the way we did in our example above. They have charts and formulas that help them calculate the compound interest quickly.) Interest compounded continuously uses a formula that involves the number "e". "e" is like "pi" in that it's an irrational number that people just found as they calculated things like growth and decay. Continuous compounding is growth of money, so it fits the "e" situation. Anyway, if you find an account that compounds continuously, you would earn even more interest. The formula for continuous compounding is A = Pe^(rt) where the rate x time is the exponent on the constant "e" (which is about 2.7). Hope this helps. -Doctor Mason, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.