...T/TH 9:30-10:50AM LASA 1: Compound Interest 1.) Result of calculations. P(t) = P(0) e^(kt) P(0) = $1000.00 K = 0.5% = 0.005 | K = 1% = 0.01 | K = 1.5% = 0.015 | P(1) = 1005.01 | P(1) = 1010.50 | P(1) = 1015.11 | P (5) = 1025.32 | P(5) = 1051.27 | P(5) = 1077.88 | P (10) = 1051.27 | P(10) = 1105.17 | P(10) = 1161.83 | Time (T(k)) when your investment is doubling K= 0.5% | T(0.5%) | Round to whole number = 139 years | Round to tenths=138.6 | K=1% | T(1%) | Round to whole number = 69 years | Round to tenths= 69.3 | K=1.5% | T(1.5%) | Round to whole number = 46 years | Round to tenths= 46.2 | 2.) What affect did changing the interest rate have on the rate at which your investment grew? Changing the interest rate from 0.5% to 1% to 1.5% increased the rate overall of the investment such that when the interest rate was 1% at 5 years the amount of 1051.27 which increased to the amount of 1077.88 at the same year at a higher interest rate of 1.5%. As the interest rate grew higher and higher, the rate of the investment also grew higher. 3.) What affect did changing the interest rate have on the doubling time (time until your deposit doubled in size)? When the interest rate was lower, the number of years at which the investment doubled from $1000.00 to $2000.00 was higher. In my opinion, doubling the amount at the interest rate of 0.5% is somewhat unrealistic because the amount of years it is taking is almost 139 years which is not possible for a person...
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...the interest rate per period: Term of Investment 13 16 8 18 14 10.5 12 annually quarterly semiannually monthly quarterly semiannually quarterly 3 20 24 72 16 18 3 Nominal (Annual) Rate (%) Interest Compounded Compounding Periods Rate per Period (%) 13 4 4 1.5 3.5 5.25 3 1. 3 years 2. 5 years 3. 12 years 4. 6 years 5. 4 years 6. 9 years 7. 9 months T11-2 REVIEW EXERCISES | CHAPTER 11—SECTION I 1. Periods 5 Years 3 Periods/Year 5 3 3 1 5 3 13 Nominal Rate 5 5 13% Rate per period 5 Periods>Year 1 2. Periods 5 Years 3 Periods/Year 5 5 3 4 5 20 Nominal Rate 16 Rate per period 5 5 5 4% Periods>Year 4 3. Periods 5 Years 3 Periods/Year 5 12 3 2 5 24 Nominal Rate 8 Rate per period 5 5 5 4% Periods>Year 2 4. Periods 5 Years 3 Periods/Year 5 6 3 12 5 72 Nominal Rate 18 Rate per period 5 5 5 1.5% Periods>Year 12 5. Periods 5 Years 3 Periods/Year 5 4 3 4 5 16 14 Nominal Rate 5 5 3.5% Rate per period 5 Periods>Year 4 6. Periods 5 Years 3 Periods/Year 5 9 3 2 5 18 10.5 Nominal Rate 5 5 5.25% Rate per period 5 Periods>Year 2 7. Periods 5 Years 3 Periods/Year 5 .75 3 4 5 3 12 Nominal Rate 5 5 3% Rate per period 5 Periods>Year 4 T11-3 REVIEW EXERCISES | CHAPTER 11—SECTION I Manually calculate the compound amount and compound interest for the following investments: Principal 2 1 3 10 12 8 annually quarterly semiannually Term of Nominal Interest Investment (years) Rate (%) Compounded Compound Amount $4,840 $11,255.09 $10,122.55 Compound Interest $840...
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...annual simple interest rate of 6%, for 10 months b) To invest 5,000€ in a bank account that offers an annual compound interest rate of 6%, for 10 months The bank pays interests once per month a) b) So, option b) is the best. 2- Prove which of the following options is the most interesting one: a) To invest 5,000€ in a bank account that offers an annual simple interest rate of 6%, for 1 year b) To invest 5,000€ in a bank account that offers an annual compound interest rate of 6%, for 1 year The bank pays interests once per month a) b) So, option b) is the best. 3- Prove which of the following options is the most interesting one: a) To invest 5,000€ in a bank account that offers an annual simple interest rate of 6%, for 10 months b) To invest 5,000€ in a bank account that offers an annual compound interest rate of 6%, for 10 months The bank pays interests once per year a) b) So, option a) is the best. 4- What do you prefer a) To receive 1,000€ today? b) To receive 1,030,3€ in 3 months? c) To receive 1,062.8€ in 5 months? The annual interest rate is 12%, and interests are paid once per month Let’s find its value in 5 months: a) b) c) 0 So, option c) is the best. 5- What do you prefer a) To invest 5,000€ for 12 months, in a bank account that offers a simple interest rate of 10% b) To invest 5,000€ for 12 months, in a bank account that offers a compound interest rate of 10% In both cases, the bank will pay interests once per year...
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...COMPOUND INTEREST Definition of Terms: Compound Interest – whenever at stipulated intervals during the term of an investment, the interest due is added to the principal and thereafter earns interest, the sum which represents the increase in the original principal at the end of the term is called compound interest. Compound Amount – it is the total amount due which is the sum of the original principal and the compound interest. Conversion Period – it is the time between successive conversions of interest into principal. Conversion periods are the following: m = 12 if conversion period is monthly m = 2 if conversion period is semi-annually m = 4 if conversion period is quarterly m = 1 if conversion period is annually Compound Interest Formula: F = P ( 1 + I )n Where: F = compound amount or Future Value or Final Amount P = original principal or Present Value i = interest rate per conversion period which is equal to the nominal rate (j) divided by the conversion period (m) n = total number of conversion periods for the whole term; number of conversion periods per year (m) multiplied by the time or term (t). EXAMPLE: 1. Determine the compound amount and interest if P5,000 is invested at 10% compounded quarterly for 4 years. Solution: Interest rate per conversion period: Total number of conversion periods: i...
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...Financial Sustainability Team C’s presentation will review 5 financial areas within ABC Co. We will first define financial sustainability; address calculating cost, revenue, and profit, the rule of 72, calculating interest, and compound interest. We will use math concepts and rationale businesses and how companies can use our math concepts and rationale to achieve financial sustainability. What is Financial Sustainability? * Define it! * Is it a buzzword? * What does it mean to an individual? * What does it mean to an organization? * Is it important for a business owner to understand financial sustainability in both personal and professional areas? Financial sustainability has become something of a buzzword in the non-government sector (NGO) sector. We believe that it’s an important financing strategy to help companies decide what opportunities and activities the organization should pursue once they develop a financial strategy (Mango Guide, n.d.). “The first step to helping an individual or business understand their financial health and well being is how we define financial sustainability? What is financial sustainability? To an entity, financial sustainability refers to the ability to sustain itself financially. To an individual, this means to financially live within one’s means” (University of Phoenix, 2010). When our team met with ABC Co. we gave first gave the chief financial officer and his team the financial sustainability...
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...Time Value of Money Table of Contents Abstract………………………………………………………………………………3 Time Value of Money………………………………………………………………..4 Future Value and Present Value…………………………………………………......5 Challenges…………………………………………………………………………...6 Summation…………………………………………………………………………..8 References…………………………………………………………………………...9 Abstract Time value of money operations are the backbone of financial decisions in business. The basics of their operation lie in interest calculations that can be used to determine the value of money five years ago, today and even well into the future. These calculations can be tricky and are weighed with outside challenges that can affect them positively and negatively and give a good framework of when, where and how money should be invested and capital allocated. Time Value of Money It is generally stated that money today is worth more than the money of tomorrow. This simple statement of finance is the basis for understanding the time value of money and how it relates to opportunity costs, sunk costs, present and future values and discount rates. (Wilson, 2010). There are many factors which affect money, but predominantly inflation, risk, and opportunity loss are the factors which affect the time value of money and are the influences which directly affect a manager’s ability to understand and use financial information relating to present and future values to make sound decisions. Future Value (Fv) and Present Value (Pv) In economics, the time value...
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...deposited in an account that pays interest compounded periodically. Often, however, people do not deposit money and then sit back and watch it grow. Rather, money is invested in small amounts at periodic intervals. Consider these problems: 1. Chrissy deposits $200 each year into a savings account that has an annual interest rate of 8% compounded annually. How much money will Chrissy have in her account after three years? Hint: Make up a table of how much she has in her account by year. 2. Ben saves $50 per month in a credit union that has an annual interest rate of 6% compounded monthly. How much money will Ben have in his account after he has made six deposits? Page 1 of 7 II. Generalization Let's generalize the situation. Suppose we deposit P dollars each payment period for n payment periods at rate of interest i per payment period. a. Consider the first deposit only. During how many payment periods does interest get applied to this investment? ____________ Using the compound interest formula, how much is this part of the investment worth? Call this quantity A1. __________________________ b. Consider the second deposit only. During how many payment periods does interest get applied to this investment? ____________ Using the compound interest formula, how much is this part of the investment worth? Call this quantity A2. __________________________ c. Generalize. Consider the kth deposit only. During how many payment periods does interest get applied to this investment? ____________...
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...should be able to: n The Interest Rate Simple Interest Compound Interest Single Amounts • Annuities • Mixed Flows Understand what is meant by “the time value of money.” Understand the relationship between present and future value. Describe how the interest rate can be used to adjust the value of cash flows – both forward and backward – to a single point in time. Calculate both the future and present value of: (a) an amount invested today; (b) a stream of equal cash flows (an annuity); and (c) a stream of mixed cash flows. Distinguish between an “ordinary annuity” and an “annuity due.” Use interest factor tables and understand how they provide a shortcut to calculating present and future values. Use interest factor tables to find an unknown interest rate or growth rate when the number of time periods and future and present values are known. Build an “amortization schedule” for an installment-style loan. n n Compounding More Than Once a Year Semiannual and Other Compounding Periods • Continuous Compounding • Effective Annual Interest Rate n n n Amortizing a Loan Summary Table of Key Compound Interest Formulas Summary Questions Self-Correction Problems Problems Solutions to Self-Correction Problems Selected References n n n n n n n n n n n 39 Part 2 Valuation The chief value of money lies in the fact that one lives in a world in which it is overestimated. —H. L. MENCKEN A Mencken Chrestomathy The Interest Rate Which would you prefer...
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...PROBLEMS 5-1A. (Compound Interest) To what amount will the following investments accumulate? a. $4,000 invested for 11 years at 9% compounded annually b. $8,000 invested for 10 years at 8% compounded annually c. $800 invested for 12 years at 12% compounded annually d. $21,000 invested for 6 years at 5% compounded annually 5-2A. (Compound Value Solving for n) How many years will the following take? a. $550 to grow to $1,043.90 if invested at 6% compounded annually b. $40 to grow to $88.44 if invested at 12% compounded annually c. $110 to grow to $614.79 if invested at 24% compounded annually d. $60 to grow to $73.80 if invested at 3% compounded annually 5-3A. (Compound Value Solving for i) At what annual rate would the following have to be invested? a. $550 to grow to $1,898.60 in 13 years b. $275 to grow to $406.18 in 8 years c. $60 to grow to $279.66 in 20 years d. $180 to grow to $486.00 in 6 years 5-4A. (Present Value) What is the present value of the following future amounts? a. $800 to be received 10 years from now discounted back to present at 10% b. $400 to be received 6 years from now discounted back to present at 6% c. $1,000 to be received 8 years from now discounted back to present at 5% d. $900 to be received 9 years from now discounted back to present at 20% 5-5A. (Compound Annuity) What is the accumulated...
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...large purchases less frequently probably prefer using the payback method. I would point out to them that the payback method although easier, they might find themselves focusing on short-term thinking because it does not account for any cash flow after payback, hence ignoring the time value of money. References: Mahar, J. (2004, November 12). Capital Budgeting [Blog post]. Retrieved from FinanceProfessorBlog website: http://financeclass.blogspot.com/2004/11/ capital-budgeting.html Hi Sabina, To financial managers compound interest is the greatest thing since sliced bread. We have learned of all the benefits when it works in our favor. Let's play devil's advocate and look at how and when compound interest can actually work against us at the personal level, small business level, or corporate level. What I am talking about is the part of the equation that looks at debt. When it comes to loans, we all know the interest that builds on an initial principal can be hard to stomach. Dealing with loads of credit card debt is a problem I have faced. It completely boggled my mind how a $1000 line of credit, turned...
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...Northwest Bank pays a quoted annual (nominal) interest rate of 4.75%. However, it pays interest (compouned) daily using a 365-day year. What is the effective annual rate of return (APY)? A. 4.75% B. 4.86% C. 5.02% D. 3.61% 14) You have $10,000 to invest. You do not want to take any risk, so you will put the funds in a savings account at the local bank. Of the following choices, which one will produce the largest sum at the end of 22 years? A. An account that compounds interest annually B. An account that compounds interest monthly C. An account that compounds interest daily D. An account that compounds interest quarterly 15) When George Washington was president of the United States in 1797, his salary was $25,000. If you assume an annual rate of inflation of 2.5%, how much would his salary have been in 1997? A. $1,025,000 B. $3,489,097 C. $954,719 D. $4,085,920 E. $2,525,548 16) Which of the following is NOT a basic function of a budget? A. Budgets indicate the need for future financing. B. Budgets allow for performance evaluation. C. Budgets provide the basis for corrective action when actual figures differ from the budgeted figures. D. Budgets compare historical costs of the firm with its current cost performance. 17) Which of the following statements about the percent-of-sales method of financial forecasting is true? A. It is the least commonly used method of financial forecasting. B. It projects all liabilities as a fixed percentage of sales. C. It is a much...
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...Lecture Quiz 1 1. Wayne Rooney received the amount of money Z at the end of 4 years when X dollar is invested at compound rate r . Z = X (1+r)t, where t is investment period. What range of interest rate (in percent) will provide the expected return, if: a. A firm is investing 80,000 for 4-year period and expects to get a return of no less than $ 200,000 and less than 500,000. (5) b. A firm is investing 100,000 for 4-year period and expects to get a return of no less than $ 200,000 and no more than 500,000. (5) 2 2. Raisa Andriana purchased a sofa for her company for $160,000. Her production company depreciated the sofa at the end of each year at the rate of 15% (annual rate) of its current value. For question (a-c) follow above information: a. What is the value of the sofa at the end of 3rd year. (2.5) b. What is the value of the sofa at the end of 5th year. (2.5) c. What is the value of total sofa depreciation at the end of 4th year. (2.5) d. What is the value of the sofa at the end of 3rd year, if the sofa is depreciated at the end of each quarter at the rate of 20% of its current value. (2.5) 3 3. In 1950, Frank Sinatra purchased a sedan from Elvis Presley for $50. Suppose the $50 was invested by Elvis Presley in 1960 at 8% rate. How much money would the (i) investment be worth & (ii) total interest accumulated in 2005 if the interest was: a. Simple Interest (2) b. Compounded annually (2) c. Compounded monthly (2) d. Compounded quarterly (2) e. Compounded continuously (2)...
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...loan, we need more mathematics. Simple Interest Discussing interest starts with the principal, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5. The total amount you would repay would be $105, the original principal plus the interest. [pic] Example: A friend asks to borrow $300 and agrees to repay it in 30 days with 3% interest. How much interest will you earn? P0 = $300 (the principal) r = 0.03 (3% rate) I = $300(0.03) = $9. You will earn $9 interest. One-time simple interest is only common for extremely short-term loans. For longer term loans, it is common for interest to be paid on a daily, monthly, quarterly, or annual basis. In that case, interest would be earned regularly. For example, bonds are essentially a loan made to the bond issuer (a company or government) by you, the bond holder. In return for the loan, the issuer agrees to pay interest, often annually. Bonds have a maturity date, at which time the issuer pays back the original bond value. Example: Suppose your city is building a new park, and issues bonds to raise the money to build it. You obtain a $1,000 bond that pays 5% interest annually that matures in 5 years. Each...
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...Time Value of Money: Simple Interest versus Compound Interest Outline I. Applications of Time Value of Money 1.1 Example One 1.2 Example Two 2. Interest 2.1 What is Interest? 2.2 Three Variables of Interest 1. Principal 2. Interest Rate 3. Time 2.3 Why is Interest Charged? 3. Simple Interest 3.1 What is Simple Interest? 3.2 Simple Interest Formula 4. Compound Interest 4.1 What is Compound Interest? 4.2 Compound Interest Formula 5. Compound Interest Tables 1. Future Value of $1 2. Present Value of $1 3. Present Value of an Ordinary Annuity of $1 4. Present Value of an Annuity due 5. Present Value of a Deferred Annuity 6. Conclusion 7. References Abstract The time value of money (TVM) is based on the principle that "a dollar today is worth more than a dollar in the future, (Mott, 2010, pp.31). Waiting for future dollars involves a cost -the cost is foregoing the opportunity to earn a rate of return on money while you are waiting" (pp.31). TVM was developed by Leonard Fibonnacci in 1202 and is one of the basic concepts of finance. One hundred dollars today has a different buying power than it will have in the future. For example, $100 invested in a savings account at your local bank yielding 6% annually will grow to $106 in one year. The difference between the $100 invested now-the present value of the investment-and its $106 future value represents the time value of money, (Spiceland...
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...Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Chapter 1 . Mathematics of Finance Contents 1. Compound Interest 2. Continuous Money Flow: Total money flow, present value, accumulated amount of money, continuous deposits. 3. Annuities 4. Amortizations and Sinking Funds Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Simple and compound interest • If you borrow money you have to pay interest on it. If you invest money in a deposit account you expect to earn interest on it. Interest can be interpreted as money paid for the use of money. • The original amount borrowed or invested is called the principal, denoted by P. Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Simple and compound interest The rate of interest r is the amount charged for the use of the principal for a given length of time, usually on a yearly (or per annum, abbreviated p.a.) basis, given either as a percentage (p per cent) or as a decimal r , i.e. r= p . 100 The total amount received after (investing) a period of time is called accumulated value. The accumulated value after t year is A(t). Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Simple and compound interest Simple interest. Simple interest is interest computed on the principal for the entire period it is borrowed (or invested). It is assumed that...
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