Compound interest and simple interest worksheet

[Pages:2]Compound interest and simple interest worksheet

Interest refers to fees charged for the right to use money that belongs to someone else. Banks often pay interest to customers on deposit accounts, while customers pay interest to lenders when they take out loans. Interest can be calculated as simple interest or compound interest. Compound interest takes into consideration the amount of money that will be earned on interest that gets added to the account. To calculate interest, you need to know the amount in the account, the interest rate on the account, how long the money remains in the account and how often the interest will be compounded. Divide the annual interest rate by 100 to convert it to a decimal. For example, if the annual interest rate is 8 percent, you would divide 8 by 100 to get 0.08. Divide the annual interest rate, expressed as a decimal, by the number of times per year interest compounds to calculate the periodic interest rate. Continuing the example, if the account compounds interest quarterly, you would divide 0.08 by 4 to get 0.02. Multiply the periodic interest rate by the balance of the account. For example, if the account has a balance of $500, you would multiply $500 by 0.02 to find the interest would be $10. Multiply the interest per period by the number of periods the money will remain in the account. Finishing the example, if you leave the money in the account for five quarters, you would multiply $10 by 5 to find the total interest would be $50. Divide the annual interest rate by 100 to convert it to a decimal. For example, if the annual interest rate equals 8 percent, divide 8 by 100 to get 0.08. Divide the annual interest rate expressed as a decimal by the number of times per year interest compounds to calculate the periodic interest rate. Continuing the example, if the account compounds interest quarterly, you would divide 0.08 by 4 to get 0.02. Add 1 to the periodic interest rate expressed as a decimal. In this example, you would add 1 to 0.02 to get 1.02. Raise that result to the Nth power, where N equals the number of periods that the money will remain in the account. In this example, if you were leaving the money in the account for five quarters, you would raise 1.02 to the fifth power to get 1.104080803. Subtract 1 from that result to calculate the total interest rate. In this example, you would subtract 1 from 1.104080803 to get 0.104080803. Multiply the total interest rate by the balance of the account to find the total interest. Finishing the example, if you had $500 in the account, you would multiply $500 by 0.104080803 to find the total interest would be $52.04. 6 second take: Ever wanted to learn more about the power of compounding interest? This video will show you how your interest will grow over time. American consumers carry $227,500 in savings, according to the Federal Reserve Bank, and that number is only rising. Considering the effect that interest can have on savings, it's essential that the average American knows how to build their savings -- and to start young. If you want to learn more about how to increase your savings without having to worry about investing more money, this video can help you learn about the power of compounding interest. Build and Personalize Your Investing Portfolio Get Your Stock Advisor Offer Here's what you'll need to enter in: Initial investment: This is how big a starting deposit you're making. Contribution amount: If you'll be making additional deposits, how much will you add, and how frequently? Not all investments require additional deposits, but many allow it. Interest rate: This is the return on your investment. Then select how frequently the interest compounds. This is how often interest will be calculated on your deposit. This can vary, and might be daily, monthly, annually, or for some other time period. Length of investment: This is how long you'll leave your investment in the account before you make a withdrawal. Here's what the results mean: Total future balance: This is how much you have in your account in total. It's a combination of your own contributions, plus whatever interest you've earned.Total interest: This is how much total interest you've earned. In other words, this is the dollar amount of the return on your investment. Total contributions: This is how much you've personally contributed, both from the start and over time (if you made additional deposits). In other words, how much you yourself have put in and saved up. Compound interest is a way of calculating interest based on your present balance. This includes all of the interest you've earned previously at set intervals called the compounding frequency (hence the name, "compound interest"). Because your returns get larger and larger over time, your balance also increases faster with compound interest than it does with other methods. At some point, your returns will be even larger than what you added to the account. This is the ultimate goal with retirement accounts--you save so much that you can live indefinitely off the earnings of your account, rather than drawing down the amount of money that you've saved. Here is how compound interest is calculated for investments in which you only make one deposit (such as a certificate of deposit, or CD): A = P (1 + r/n)nt A is the total amount of money you have at the endP is your initial investment amountr is your interest rate, expressed as a decimaln is how many times your interest is compounded each yeart is how many years your money is invested For example, let's say you deposit $1,000 into a CD at an interest rate of 2.5% APY and let it sit for five years, compounded monthly. Here's how you would plug that into your calculator: 1000 * (1 + (0.025 / 12)) ^ (12 * 5) = $1,133 After five years, you'd have earned $133 in interest. The compounding frequency has a big effect on how fast you earn interest, too. The more often your interest is compounded, the faster it adds up. For example, consider two investments that pay a 5% interest rate, but one is compounded monthly and the other is compounded annually. You'll earn more interest with the investment that compounds monthly because that's 12 chances for your balance to increase throughout the year, rather than once at the end. With simple interest, your interest earnings are only calculated based on your initial balance. Your balance will still grow, but it'll increase at a slower rate because those extra interest earnings aren't taken into account when calculating how much interest you're owed. Compound interest is most often used with investments. Rather than earning money based solely on what you've put in (your principal, in other words), you can earn money from your previous earnings also. This allows your balance to grow much faster, and it comes in handy, especially for long-term investments like retirement accounts. In fact, if you start saving for retirement while you're young, by the time you retire, your retirement savings could even be made up mostly of market returns, or earnings, rather than what you've personally set aside. This is why it's so important to start saving while you're young. Rather than having to work yourself to earn those dollars, you can set up your dollars to start working for you over the years. That way, you won't have to work as hard or as long. Most types of investments use compound interest. For example, interest-bearing checking accounts, savings accounts, and CDs (or share certificates, at credit unions) all commonly use compound interest when calculating how much they owe you. It's still worth checking the fine print, however, because you don't want to get trapped in an investment that gives you less than you thought you were earning. The biggest benefit of using a compound interest calculator is being able to tell exactly how much your money will grow in real, tangible dollars. After all, it's easy enough to understand that a higher rate is better--but what does that rate actually mean over time? The compound interest calculator can tell you exactly how much money you'll have in the future. You can use that number to see whether a particular investment is really worth your effort, and to plan for how you might eventually use that money. For example, if a particular investment will only reward you with an extra $1.50 but takes an hour of your time to set up, is it really worth it? Or, if you set aside an extra $100 toward your IRA from each paycheck, how many extra dollars would that grow into by the time you retire? You can use that number as motivation to save even more. Calculating simple interest is an essential skill for anyone who maintains a bank account, carries a credit card balance, or applies for a loan. The free printable worksheets in this lesson will improve your homeschool math lessons and help your students become better at calculations. This collection of worksheets will also help students understand the process using word problems. Answers are provided for each of the five worksheets on the second page for ease of grading. Before having students start on the worksheets, explain that when you borrow money, you have to repay the amount you borrowed as well as any added interest charges, which represents the cost of borrowing. In the same way, explain to students that when you lend money or deposit funds in interest-bearing accounts, you typically earn interest income for making your money available to other people. D. Russell Print the PDF: Simple Interest Worksheet No. 1 In this exercise, students will answer 10 word problems about calculating interest. These exercises will help homeschoolers learn how to calculate the rate of return on investments and illustrate how interest can accrue over time. Students will answer such questions as, "How much interest does a $318 investment earn at 9 percent over one year?" Explain to students that the answer would be $28.62 because $318 x 9 percent is the same as $318 x 0.09, which equals $28.62. Explain to students that they would have to pay this amount of interest in addition to repaying the principal, the amount of the original loan, $318. D. Russell Print the PDF: Simple Interest Worksheet No. 2 These 10 questions will reinforce the lessons from worksheet No. 1. Homeschoolers and other students will learn how to calculate rates and determine interest payments. For this PDF, students will answer word problem questions such as: "If the balance at the end of eight years on an investment of $630 that has been invested at a rate of 9 percent is $1,083.60, how much was the interest?" If students are struggling, explain that calculating this answer involves only simple subtraction, where you subtract the initial investment of $630 from the ending balance of $1,083.60. Students would set up the problem as follows: $1,083.60 ? $630 = $453.60 Explain that some of the information in the question was extraneous and not necessary to solve the problem. For this problem, you don't need to know the years of the loan (eight years) or even the interest rate; you only need to know the beginning and ending balance. D. Russell Print the PDF: Simple Interest Worksheet No. 3 Use these word questions to continue practicing how to calculate simple interest. Students can also use this exercise to learn about the principal, rate of return (the net gain or loss on an investment over a specified time), and other terms commonly used in finance. D. Russell Print the PDF: Simple Interest Worksheet No. 4 Teach your students the basics of investing and how to determine which investments will pay the most over time. This worksheet will help your homeschoolers polish their calculating skills. D. Russell Print the PDF: Simple Interest Worksheet No. 5 Use this final worksheet to review the steps for calculating simple interest. Take time to answer questions your homeschoolers may have about how banks and investors use interest calculations.

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