Download Math 113 Notes Chapter 1: Simple Interest I = P * i * t I = $600

Math 113 Notes Chapter 1: Simple Interest Definitions: 1.
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Money borrowed or invested is called principal The charge for the use of money or the returns on invested money is interest The length of the loan or investment is the term Simple interest -­‐ interest is paid or earned only the original principal Compound interest ʹ interest is paid or earned both on the original principal and on interest gained period by period Simple Interest Formula I = P * i * t I = interest amount P = principal i = interest rate in decimal form t = term of loan in years Example 1: If $600 is borrowed at 6.25% for 8 months, how much interest is paid? I = ? P = $600 I = $600 * .0625 * 8/12 i = .0625 I = $25 t = 8/12 (DO NOT ROUND THIS OFF) Example 2: If the interest charged on a 20 week loan of $800 is $45, what interest rate is charged? I = $45 $45 = $800 * i * 20/52 P = $800 i = 45 / (800 * (20/52)) i = ? i = .14625 i = 14.625% t = 20/52 Types of Time (days) (numerator of t) 1. Exact Time (Green Handout) ʹ count the exact number of days between the two dates 2. Approximate Time ʹ works under the idea of 30 days in each month x Whole # of months * 30 x dŚĞŶ͙ĂĚĚŽƌƐƵďƚƌĂĐƚηŽĨĚĂLJƐƚŽŐĞƚƚŽƚŚĞĐŽƌƌĞĐƚĚĂƚĞ Example 3: Find the exact time and the approximate time between: (a) May 14, 2003 and Sept. 22, 2003 x Exact x Days in calendar year where May 14 lands = 134 x Days in calendar year where Sept. 22 lands = 265 x Since these are in the same year (2003) we can calculate 265 ʹ 134 = 131 days x Approximate x 4 months (30) = 120 days + 8 days = 128 days o The 8 days above is the difference between the 22nd day and the 14th day (b) October 25, 2003 and March 17, 2004 x Exact x Days in calendar year where October 25 lands = 298 x Days in calendar year where March 17 lands = 76 x Since these dates are NOT in the same year o Move the $ to the end of the current year and add days in the following year by calculating (365-­‐298) + 76 = 143 days o IF this asked you to solve for March 17, 2005 you would simply add 365 to the formula above x Approximate x 5 months (30) = 150 days x Subtract 8 days from 150 to get 142 days Types of Interest (denominator of t) 1. Ordinary interest: divide by 360 2. Approximate time: divide by 365 3. 4 Versions of t Exact time 360 Approx. time 360 ĂŶŬĞƌ͛ƐZƵůĞ Exact time 365 Approx. time 365 Example 3 (see above): t = 131/360, 131/365, 128/360, 128/365 When should we use days? (i)
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If the directions say to do so hĨƚŚĞ͞ĚĂƚĞƐ͟ĚŽŶŽƚŵĂƚĐŚƵƉ;ŝ͘Ğ͘ϱͬϭϰÆ 9/22 need days, 5/14 Æ 9/14 do not need days) Example 4: Luke borrowed $450 on April 18 and agrees to pay it back with 7.25% interest on August 22. How much interest is charged? Give all 4 answers. April 15 = day 108 August 22 = day 234 Exact time Æ 234 ʹ 108 = 126 days Approximate Æ 4 months (30)+ 4 days = 124 days 4 versions of t: 126 360 124 360 ĂŶŬĞƌ͛ƐZƵůĞ I = $450 * .0725 * 126/360 I = $11.42 I = $450 * .0725 * 124/360 I = $11.26 126 365 124 365 I = $450 * .0725 * 126/365 I = $11.24 I = $450 * .0725 * 124/365 I = $11.08 Future Value (or Amount) ʹ the value of some money at any date in the future when compared to the date at which we know its value Amount = principal + interest S = P + I S = P + P*i*t S = P (1+i*t) Example 1: What amount is payed t clear a $975 loan is money is borrowed at 6.5% for 18 weeks? S = ? P = $975 i = .065 t = 18/52 S = $975 * .065 * 18/52 S = $996.94