Introduction We have all earned interest on money deposited in a savings account or paid interest on a credit card, but do you know how the interest was calculated? The two most common types of interest are simple interest and compound interest. As its name implies, simple interest is the easiest type to calculate. It is the interest that is paid only on the principal, or the amount that was put into or borrowed from the bank. In contrast, compound interest is charged (or paid) on the interest as well as the principal. The table below compares an investment of $10,000 at a 7% interest rate when it is calculated using both the simple and compound interest methods. Notice the ending balance of both calculations at the end of five years. Simple Interest Compound Interest Start 10,000.00 10,000.00 After 1 year 10,700.00 10,700.00 After 2 years 11,400.00 11,449.00 After 3 years 12,100.00 12,250.43 After 4 years 12,800.00 13,107.96 After 5 years 13,500.00 14,025.52 Calculating In order to calculate simple interest, there are three things that we need to know: Principal: the amount put into the bank or borrowed from the bank Rate: Time: interest rate for one year. This is usually expressed as a percentage. To do the calculations, convert the percentage to a decimal. how long the money is in a savings account or how long it will take to pay back a loan (expressed in years) The formula that is used to calculate simple interest is: INTEREST = PRINCIPAL x RATE x TIME OR I = P x R x T Page 1 of 10
Example 1 Interest (I) Computers 4 U deposits $5000.00 in a savings account that pays an annual interest rate of 6.5%. How much simple interest will Computer's 4 U earn in one year? What is the total amount that will be in the account at the end of one year? 1. Find the PRINCIPAL: $5000.00 2. Find the RATE: 6.5% (or.065) 3. Find the TIME: 1 year 4. Find the INTEREST PRINCIPAL x RATE x TIME $5000.00 x 6.5% x 1 = $325.00 5. The total amount in the bank account at the end of one year is: Example 2 Interest (1) $5000.00 + $325.00 = $5325.00 Suppose you deposited $25,000.00 in a bank with a 5% annual interest rate. Using the simple interest method, how much interest would you receive at the end of two years? What is the total amount that would be in your account at the end of the year? 1. Find the PRINCIPAL: $25,000.00 2. Find the RATE: 5% or.05 3. Find the TIME: 2 4. Find the INTEREST PRINCIPAL x RATE x TIME $25000.00 x.05 x 2 $1250.00 x 2 = $2500.00 5. The total amount in the bank account at the end of one year is: $25,000.00 + $2,500.00 = $27,500.00. Page 2 of 10
Exercise Interest (I) in years Calculate the simple interest for the stated amounts, rates, and times. Instructions The answer must be rounded up to 2-decimals. Principal Rate Time Simple Interest $8,000.00 13% 2 $ 2,080.00 $1,550.00 16% 3 $ 744.00 $2,500.00 9.5% 1 $ 237.50 $6,450.00 11.65% 2 $ 1,502.85 $4,850.00 12.5% 1 $ 606.25 $5,500.00 7.5% 4 $ 1,650.00 $2,500.00 22% 1 $ 550.00 $6,850.00 9.25% 2 $ 1,267.25 $10,000.00 8.50% 3 $ 2,550.00 $9,750.00 9.25% 2 $ 1,803.75 Page 3 of 10
Calculating for a Period of Less than One Year In the previous example, the time was expressed in years. Often, interest is paid for less than one year, so we must express this duration in yearly terms. If the interest is paid for a number of days, it can be expressed as follows: Number of days/365 If the interest is paid for a number of months, it can be expressed as follows: Number of months/12 Example - Calculating for a Number of Days Calculate the simple interest on $6,000 that is borrowed for 30 days at an annual rate of 4.5%. Solution Since the interest rate is for one year, we must also express the time in yearly terms. Since there are 365 days in a year, we know that the duration is 30/365. 1. Find the PRINCIPAL: $6,000.00 2. Find the RATE: 4.5% (or.045) 3. Find the TIME: 30/365 4. Find the INTEREST PRINCIPAL x RATE x TIME $6,000.00.00 x.045 x 30/365 $270.00 x 30/365 $270.00 x 0.8219178082 = $22.19 Page 4 of 10
Exercise Interest (I) in days Calculate the simple interest for the stated amounts, rates, and times. Instructions The answer must be rounded up to 2-decimals. Principal Rate Time (in days) Simple Interest $8,000.00 13% 90 $ 256.44 $1,550.00 16% 180 $ 122.30 $2,500.00 9.5% 30 $ 19.52 $6,450.00 11.65% 360 $ 741.13 $4,850.00 12.5% 45 $ 74.74 $5,500.00 7.5% 120 $ 135.62 $2,500.00 22% 65 $ 97.95 $6,850.00 9.25% 350 $ 607.59 $10,500.00 8.50% 66 $ 161.38 $9,750 9.25% 220 $ 543.60 Page 5 of 10
Example - Calculating for a Number of Months. How much interest would you pay on a $5,000 loan with a 9.25% interest rate for 9 months? Solution The duration must be expressed in yearly terms. Since there are 12 months in a year, we can conclude that the duration is 9/12. 1. Find the PRINCIPAL: $5,000.00 2. Find the RATE: 9.25% (or.0925) 3. Find the TIME: 9/12 4. Find the INTEREST PRINCIPAL x RATE x TIME $5000.00 x.0925 x 9/12 $462.50 x 9/12 $462.50 *0.75 $346.88 Page 6 of 10
Exercise Calculate the simple interest for the stated amounts, rates, and times. Instructions The answer must be rounded up to 2-decimals. Principal Rate Time (in Months) Simple Interest $8,000.00 13% 2 $ 173.33 $1,550.00 16% 3 $ 62.00 $2,500.00 9.5% 1 $ 19.79 $6,450.00 11.65% 8 $ 500.95 $4,850.00 12.5% 6 $ 303.13 $5,500.00 7.5% 9 $ 309.38 $2,500.00 22% 7 $ 320.83 $6,850.00 9.25% 6 $ 316.81 $10,000.00 8.50% 11 $ 779.17 $9,750.00 9.25% 2 $ 150.31 Page 7 of 10
Earning Interest on an Investment Calculating TIME (Duration) How long will it take... Now that you know how to calculate simple interest, let s see how to calculate how long it will take to earn a specific amount of interest on an investment. For instance, if you have $50,000 to invest, with an interest rate of 8%, how long will it take you to earn $10,000? To calculate the time it will take, we will first calculate the interest for one year. 50,000 * 8% = 4,000 Now, divide the total amount of interest that you would like to earn, by the amount you would earn in one year. 10,000 / 4,000 = 2.5 It would take 2.5 years to earn $10,000 on a $50,000 investment with an interest rate of 8%. Based on this information, the formula that can be used is: Time = Interest / (Principal * Rate) Time is the amount of time it will take to earn the interest. Sometimes called Duration. Interest is the amount that you want to earn. Principal is the initial investment. Also referred to as Capital. Rate is the interest rate that you will earn on the investment. Page 8 of 10
Exercise Calculate how long it would take to earn the specified amount of interest on each of the following investments. Round the length of time to 2 decimal places. Instructions The answer must be rounded up to 2-decimals. Capital Rate Interest Time $100,000 7.5% $15,000 2.00 $35,000 5.3% $2,500 1.35 $50,000 8% $1,250 0.31 s$125,000 11.3% $25,000 1.77 $25,000 4.35% $1,000 0.92 $20,000 5.25% $2,500 2.38 $150,000 6.75% $10,000 0.99 $200,000 3.69% $30,000 4.07 $175,000 4.08% $20,000 2.80 $75,000 5.35% $18,000 4.49 Page 9 of 10
Practical Applications 1. WQCC Computers invests $18,000 with a simple interest rate of 6.5% for 5 years. a) Calculate the simple interest to be paid. $5,850.00 b) What is the total amount WQCC Computers will receive at the end of the term.? $23,850.00 2. Neptune Yacht Outfitters deposits $55,000 in a savings account for a period of 6 months with an interest rate of 5%. a) Calculate the simple interest they will receive at the end of the period. $1,375.00 b) What is the total amount they will receive at the end of the period? $56,375.00 3. Computers 4 U took out a simple interest loan for $25,000 at an interest rate of 6.5% for 5 years. a) How much interest will they have to pay? $8,125.00 b) What is the total amount they will have to pay back? $33,125.00 4. European Coffee House places $35,000 in a savings account with an interest rate of 4% for 120 days. a) Calculate the simple interest they will earn. $460.27 b) What is the total amount they will receive at the end of the term? $35,460.27 5. Using the simple interest method, how long will it take for $1,000 to amount to $1,900.00 with an interest rate of 9% 10 years (revised answer) 6. WQCC Computers borrowed $5000.00 at a 9% simple interest rate and made monthly payments for 5 years. Calculate the following: a) The amount of interest to be paid $2,250.00 b) The total amount to be paid back $7,250.00 c) The monthly payment amount (think..) $120.83 Page 10 of 10