Exam 1_Study Guide.pdf - Math 1300 Spring 2018 Your Name...

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Math 1300 Your Name: Spring 2018 Exam 1 - Study Guide Warning: This study guide is a brief overview of some of the concepts, algorithms and problem solving procedures that will be tested by Exam 1. The examples below are NOT comprehensive. Students who wish to do well on Exam 1 should rework all MyMathLab homework problems using the Practice and Review feature until mastery is achieved. 10.1 Interest Future Value and Present Value (One-Time Deposit) F = Future Value P = Present Value i = r m = Interest Rate Per Period (annual interest r divided by compoundings per year m ) n = mt = Number of Interest Periods (compoundings per year times number of years) F = (1 + i ) n P (1) P = F (1 + i ) n (2) Effective Rate - APY (Used to Compare Rates with Different Compoundings Per Year) r eff = APY = Effective Rate of Interest or Annual Percentage Yield (Simple Interest Rate Yielding Same Amount of Interest as given Compound Rate) r eff = APY = (1 + i ) m - 1 (3) Example: If you had invested $ 3000 on January 1, 2009 at 4 . 0% compounded quarterly, how much would you have on April 1, 2015? Solution: i = . 04 4 = . 01 n = (4)(6) + 1 = 25 F = (1 + . 01) 25 (3000) = $3847 . 30
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Math 1300, Exam 1 Study Guide 2 Example: Calculate the effective rate for 8 . 1% compounded monthly. Solution: i = . 081 12 = . 00675 r eff = (1 + . 00675) 12 - 1 = 8 . 41% Example: On January 1, 2006 a deposit was made into a savings account paying interest compounded semiannually. The balance on January 1, 2009 was $ 14,000.00 and the balance on July 1, 2009 was $ 14,280.00. How large was the deposit? Solution: i = 280 . 00 14 , 000 . 00 = . 02 n = (2)(3) = 6 P = 14 , 000 (1 + . 02) 6 = $12 , 431 . 60 10.2 Increasing and Decreasing Annuities Future Value of Increasing Annuity (Multiple Deposits at End of Consecutive Interest Periods) F = Future Value i = r m = Interest Rate Per Period (annual interest r divided by compoundings per year m ) n = mt = Number of Interest Periods (compoundings per year times number of years) R = Payment Amount (or Deposit Amount) F = (1 + i ) n - 1 i · R (4) New Balance in Increasing Annuity Given Previous Balance (Not Provided on Exam) B new = New Balance in Increasing Annuity B previous = Balance in Increasing Annuity at End of Last Period i = r m = Interest Rate Per Period (annual interest r divided by compoundings per year m ) R = Payment Amount (or Deposit Amount) B new = (1 + i ) B previous + R
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Math 1300, Exam 1 Study Guide 3 Present Value of Decreasing Annuity (Multiple Withdrawals at End of Consecutive Interest Periods) P = Present Value i = r m = Interest Rate Per Period (annual interest r divided by compoundings per year m ) n = mt = Number of Interest Periods (compoundings per year times number of years) R = Payment Amount (or Deposit Amount) P = 1 - (1 + i ) - n i · R (5) Example: Calculate the rent of a decreasing annuity at 9 . 0% compounded quarterly with payments made every quarter year for 7 years and a present value of $ 110,000. Solution: i = . 09 4 = . 0225 n = (4)(7) = 28 110 , 000 = 1 - (1 + . 0225) - 28 . 0225 · R R = $5337 . 78 Example: At the end of each month, $ 400 is deposited into a savings account paying 2 . 8% interest compounded monthly. The balance after 14 years will be $ 82,159.19. What is the amount of interest earned over that period of time?
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