# 5-1 - Chapter 5.1 Compound Interest Simple interest is...

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Simple interest is interest that accumulates only on the original principal. If P is the principal (amount deposited), r is the rate of simple inter- est, and t is the number of years the amount earns interest, then the interest earned, I is given by the following formula: I = Prt The accumulated amount we will have, A , is the sum of the prin- cipal and the interest. In symbols, A = P + I = P + Prt = P (1 + rt ). Example: I deposit \$1000 in an account paying 8% simple interest. I deposit this money for Fve years. ±ind the total amount of interest earned, and the accumulated amount. We have that P = 1000, r = 0 . 08, and t = 5. This gives us: I = Prt = (1000)(0 . 08)(5) = 400 \$400 of interest will be earned. We have that P = 1000 and I = 400. This gives us: A = P + I = 1000 + 400 = 1400 \$1400 is the accumulated amount. Usually, our account is a compound interest account. This means that interest is earned on the principal, as well as on any interest accumulated thus far. Example: In our last example, we deposited \$1000. Suppose that the interest we earn is compound interest. How much money will we have after 5 years. Let A 1 be the amount at the end of the Frst year, A 2 , be the amount at the end of the second year, and so on. With t = 1, we have that the amount after 1 year will be given by: A 1 = P (1 + rt ) = P (1 + r ) ±or the second year, the new principal will be the amount at the end of the Frst year. In other words, we will have that: A 2 = P (1 +

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## This note was uploaded on 02/05/2011 for the course MATH 377 taught by Professor Stephenlang during the Spring '11 term at University of Victoria.

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5-1 - Chapter 5.1 Compound Interest Simple interest is...

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