Why Study Math? – The Mathematics of Finance – Interest – Part I


All right kids. So you hate math and you don’t care whether you do well in this subject or not. But know one thing. Mathematics is the language of money. That’s right. Whether we’re talking interest on CD’s or bonds, dividend yields on stocks, or returns on investment for a business venture, math is the lingua franca–or universal languge. So remember that if you don’t learn math well, you just might be giving an opportunity to some other hungry kid who wants to own more Jordan sneakers than you. Simply put: if you want the goodies in life, you best learn now that math can rule you to the land of fruit and nuts.

Indeed mathematics is the subject that explains how money accumulates and grows over time. What we’re talking about here is interest–compound interest specifically. You see, when you go to your neighborhood bank and place a sum of money, the bank pays you for your generosity in letting the bank use that money. What the bank pays you is called interest and the way this is calculated is with the compound interest formula. This formula is the portal, or gateway, to more elaborate financial calculations: annuities, perpetuities, mortgages, and other financial instruments all hinge on this formula. Because of its importance, the compound interest formula is a necessary part of every person’s know-how.

Let’s examine this formula using a basic example. Suppose you place $1,000 at your local bank. The bank is paying a healthy 6% interest for your funds. If the bank were to compound this money yearly, then you would calculate your accumulated amount by using the formula A = P*(1 + i), where A = the accumulated amount, i = the interest rate or.06, and P = the principal or $1,000. When we plug these values into the formula we acquire A = $1,060. consequently at the end of the year you will have earned $60 in interest and your new balance will be $1,000 + $60 or $1,060.

If we keep this money with the bank for another year, we will receive interest on, not $1,000, but on $1,060. The accumulated amount at the end of the second year will be A = $1,060*(1 +.06) or $1,123.60. To find the interest received over the second year we need only subtract the balance at the beginning, or $1,060. consequently we acquire $63.60 as the interest received over year 2. Notice that this is $3.60 more than the interest received from the first year. This is where the term compound interest comes from. basically we are compounding interest on top of interest to get more interest each year.

We could have obtained the balance at the end of the second year by simply using the formula

A = P*(1.06)^2. If we plug in $1,000 for P and do the calculation, we arrive at $1,123.60. If we want to know the balance at the end of the third year, we use

A = P*(1.06)^3. For the balance at the end of n years, we use A = P*(1.06)^n, and we consequently arrive at the general compound interest formula.

In the next article, we will look at different compounding periods and the net effect on the accumulated value of your money. Yes it is wise to know math, particularly when it comes to the mathematics of finance. See you next time…

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