Answer the following 3 questions:

1. How many years will it take to double your money at 12% interest?
2. How many years will it take to double your money at 6% interest?
3. What interest rate is required to double your money in 36 years?

The Time Value of Money (interest rates and time) are central to most aspects of finance. Everything from Treasury Bills, Notes and Bonds to startups to capital structure revolves around the time value of money. Interest rates can be a tail wind or a head wind (credit card debt). Instruments like negative amortization mortgages can threaten the financial well-being of a household. Even the United States budget is becoming susceptible to onerous levels of interest expense - a topic you will be hearing with increasing coverage. It is crucial that you master this assignment, not only for the final exam, but for your career work and personal life. Given the Thanksgiving holiday week, the due date of this assignment will be Tuesday, November 29th at 11:59 pm. However, please allow ample time for this work and start as soon as possible. What is compound interest? Success in corporate and personal finance requires a working understanding of the magic of "compound interest." In the simplest explanation, compound interest includes the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25. Not only did you earn $5 on the initial $100 deposit, you also earned $0.25 on the $5 in interest. While 25 cents may not sound like much at first, it adds up over time. Even if you never add another dime to that account, in 10 years you'll have more than $162 thanks to the power of compound interest, and in 25 years you'll have almost $340. People who have had any experience with compounding are impressed with its power over long periods. We can show how by looking at the stock market. Ibbotson and Sinquefield calculated what the stock market returned as a whole from 1926 through 2020. They find that $1.00 placed in large U.S. stocks at the beginning of 1926 would have been worth $10,944.66 at the end of 2020. This 10.29% compounded annually for 95 years - that is: 1.10299% = $10,944.66. This example illustrates the great difference between compound and simple interest. At 10.29% compounded annually for 95 years is $10.77 (=$1 + 95 x $.1077) This is quite below the $10,944.66 that was obtained by reinvestment of all dividends and capital gains. The results are more impressive over even longer periods. A person with no experience in compounding might think that the value of $1 at the end of 190 years would be twice the value of $1 at the end of 95 years, if the yearly rate of return stayed the same. Actually the value of $1 at the end of 190 years would be the square of the value of $1 at the end of 95 years. That is, if the annual rate of return remained the same, a $1 investment in common stocks would be worth $119,785.582.52 (=$1 x 10,944.66 x 10,944.66) We can compound much more frequently than once per year. Figure 4.11 Annual, 4 Interes Interest earned 13 6 w Dollars Dollars Interest earned 2 2 2 3 Years Years Years Annual compounding Semiannual compounding Continuous compounding When cash is invested at compound interest, each interest payment is reinvested. With simple interest the interest is not reinvested. Benjamin Franklin's statement, "Money makes money and the money that money makes makes more money." is a colorful way of explaining compound interest. The difference e between compound interest and simple interest is illustrated in below. In this example, the difference does not amount to much because the loan is for $1. If the loan were for $1 million, the lender would receive $1,188,100 in two years' time. Of this amount, $8,100 is interest on the interest. The lesson is that those small numbers beyond the decimal point can add up to large dollar amount when the transactions are for large amounts. In addition, the longer-lasting the loan or the greater the interest rate, the more important interest on interest becomes. Simple and Compound Interest $1-395 $1.09 $1 ear 2 years 3 years The blue-shaded area indicates the difference between compound and simple interest. The difference is substantial over a period of many years or decades.The general formula for an investment over many period can be written as follows: Problem #1 Future Value of an Investment Fv=l>v>