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Interest Overview Investment word problems will either involve simple or compound interest. In these problems, an individual deposits a specific amount of money, called the “principal,” into a bank account that has a particular interest rate. The account accrues interest over a period of time, during which money is paid into your account by the bank. Basically, the bank uses your money for investments and pays you for the use of your money (though not very much). The interest rate is a percentage that is governed by a time cycle, such as an annual rate (the interest is paid once a year). There are two basic types of interest: Simple interest means that the account accrues interest after a certain amount of time has passed. Compound interest means that the account accrues interest after each time cycle, increasing the principal every time cycle. The word problem will state whether the account is a simple or compound interest account and will state the time cycle of the interest rate. Simple Interest The formula for calculating simple interst is: I = RPT I is the interest earned P is the principal deposited into the account R is the interest rate T is the time Additionally, the time cycle must match for the interest rate, R, and the time, T. If a simple interest question asks for the total amount in the account after interest has accrued, you will need to calculate I and then add it to the current principal, P. This new amount is usually represented as A. In other words: A = P + I Look at the following example problem: You deposit $100 into an account that has an annual simple interest rate of 5%. How much interest is accrued after three years? Solution P is $100 R is 5% or 0.05 T is 3 years I = (100)(.05)(3) = $15, which is the correct answer. Compound Interest The formula for calculating compound interest is: A = P(1+R)T A is the final amount of money in the account after acrruing interest P is the principal deposited into the account R is the interest rate T is the time Again, the time cycle must match for the interest rate, R, and the time, T. If a compound interest question asks how much interest was accrued on the account, you will need to find the difference between A and P. In other words: A - P = I Look at the following example problem: You deposit $100 into an account that has an annual compound interest rate of 5%. How much interest is accrued after three years? Solution P is $100 R is 5% or 0.05 T is 3 years A = (100)(1 + .05)3 = (100)(1.05)3 = (100)(1.157625) = 115.76 115.76 - 100 = $15.76, which is the correct answer How to Approach Interest Problems When dealing with simple or compound interest problems, you may have to read through the word problem multiple times to find all the information required to solve it (such as I, P, R, and T). In a simple interest problem, if you are instructed to find the interest accrued over some time period, use the equation I = PRT. If you are instructed to find the total amount, then first solve for I, and then add I + P to find A. In a compound interest problem, if you are asked to find the total amount after some period of time, then use the equation P(1 + R)T. If you are instructed to find the interest accrued over some time period, then first use the equation P(1 + R)T to find A and then calculate A - P. Make sure to read the problem carefully to determine what value you are being asked to find! Practice Problems If $250 is deposited into an account with an annual simple interest rate of 15%, how much interest will be earned after 4 years? If an account earns $420 in interest after 7 years and has annual simple interest rate of 10%, how much money was deposited? If $500 is deposited into an account with an annual compound interest rate of 10%, how much money is in the account after 2 years? If $40,000 is deposited into an account with an annual compound interest rate of 5%, how much money is in the account after 2 years? John has $50.00 in his bank account, which has a simple interest rate of 20% per year. How much money is in John’s account after 5 years? a) $70 b) $80 c) $90 d) $100 A bank is offering a simple interest account plan where you double the money in your account after 10 years. If you deposit $1,000,000 into your account, what is the simple interest rate per year that the bank is offering? a) 9% b) 10% c) 11% d) 12% Frank invests $1.00 in a bank account with a compound interest rate of 50% per year. How much money is in Frank’s account after 3 years? a) $3.28 b) $3.38 c) $3.48 d) $3.58 Geraldo invests $100.00 into a bank account with a compound interest rate of 300% per year. How much money is in his account after six months? a) $200 b) $300 c) $400 d) $500 Answers to Practice Problems $150 $600 $605 $44,100 D B B A
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