*Compound Interest/Discount* Compound Interest When you borrow money from a bank‚ you pay interest. Interest is really a fee charged for borrowing the money‚ it is a percentage charged on the principle amount for a period of a year - usually. If you want to know how much interest you will earn on your investment or if you want to know how much you will pay above the cost of the principal amount on a loan or mortgage‚ you will need to understand how compound interest works. * Compound interest
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Continuously Compounded Interest Mathematics: MATH650 section 02 Wendy Forbes April 27‚ 2010 We often hear people say that we should let our money work for us. Using money or capital for income or profit is called an investment. An accountant manages a company’s money. Then‚ managers or company investors review their reports to find out the financial status. The demand for accountants increases as more private companies are established. In addition‚ there are always new and changing
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COMPOUND INTEREST Making or Spending Money SIMPLE INTEREST FORMULA If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r‚ expressed as a decimal‚ then interest I charged is I Pr t This interest is not used very often. Interest is usually compounded which means interest is charged or given on the interest and the principal. Simple Interest Example COMPOUND INTEREST Payment Periods: Annually Once per year Semiannually Twice per year Quarterly
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13.1 Compound Interest • Simple interest – interest is paid only on the principal • Compound interest – interest is paid on both principal and interest‚ compounded at regular intervals • Example: a $1000 principal paying 10% simple interest after 3 years pays .1 3 $1000 = $300 If interest is compounded annually‚ it pays .1 $1000 = $100 the first year‚ .1 $1100 = $110 the second year and .1 $1210 = $121 the third year totaling $100 + $110 + $121 = $331 interest 13.1 Compound Interest Period
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commencing at age 60 and ending at age 67 Plan 1: V0 * (1.06)42 = 3‚000‚000 V0 = 3‚000‚000/(1.06)42 V0 = $259‚582.20 Plan 2: V0 * (1.06)17 = 3‚000‚000 V0 = 3‚000‚000/(1.06)17 V0 = $1‚114‚093.26 Plan 3: C * Annuity Compound Factor (6%‚ 37) = 3‚000‚000 C * [((1.06)37 – 1)/0.06] = 3‚000‚000 C *127.27 = 3‚000‚000 C = $23‚572.28 Plan 4: C * Annuity Compounding Factor (6%‚17) = 3‚000‚000 C * 28.21 = 3‚000‚000 C = $106‚334.41 Plan 5: C * Annuity
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A) B) Answer C) D) 1. What is the simple interest for a principal of $620 invested at a rate of 7% for 3 years? $173.60 $130.20 $172.60 $129.20 A) B) C) Answer D) E) 2. If you borrow $1100 for 5 years at 14% annual simple interest‚ how much must you repay at the end of the 5 years? $770.00 $2215.13 $2117.96 $77‚000 $1870.00 A)Answer B) C) D) 3. How much interest is earned in 5 years on $2‚900 deposited in an account paying 7.1% interest‚ compounded quarterly? $1‚223.07 $1‚186.44 $266
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Entire Review Problems Cumulative- Practice 1. At a certain car wash‚ 40 more cars than vans go through on a typical day. If each car pays $12 and each van pays $16 and the total earned per day is $2244‚ find the number of vans that go through the wash. 2. a) In the Fine Company‚ the CEO must invest in 30% more shares than the CFO. The shares sell for $10.20 each and the total value of the shares owned by the two of them is $132 549. Find the number of shares owned by the CEO.
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because log(0.1) = -1 log(1) = 0 log(100) = 2 log(1000) = 3 So the graph will be much easier to read. Logarithms are used in a lot of places to scale numbers when there’s a big range between the smallest and the largest numbers of interest‚ which makes them easier to talk about. y=yi x e^-kt where: y - different between temprature of body and the constant temp of room yi - initial temprature difference of body and room e - eulers number (2.718...) t - time in mins k -
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COMPOUND INTEREST ASSIGNMENT - 1 1. Mr. Dubey borrows Rs 1‚00‚000 from State Bank of India at 11% per annum compound interest. He repays Rs 41‚000 at the end of first year and Rs 47‚700 at the end of the second year. Find the amount outstanding at the beginning of the third year. 2. What sum of money will amount to Rs 9261 in 3 years at 5% per annum compound interest? 3. The simple interest on a sum of money for 2 years at 4% per annum is Rs 340. Find (i) the sum of money and (ii) the compound
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Chapter 5‚ 6 Review 1. You invested $1‚650 in an account that pays 5 percent simple interest. How much more could you have earned over a 20-year period if the interest had compounded annually? A. $849.22 B. $930.11 C. $982.19 D. $1‚021.15 E. $1‚077.94 2. Today‚ you earn a salary of $36‚000. What will be your annual salary twelve years from now if you earn annual raises of 3.6 percent? A. $55‚032.54 B. $57‚414.06 C. $58‚235.24 D. $59‚122.08 E. $59‚360.45 3. You hope to buy your dream
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