An Introduction to the Mathematics of Money potx

[...]... prefer to have $100 now or $100 a year from now? Even though the amounts are the same, most people would prefer to have $100 now because of the interest it can earn Thus, whenever we talk of money we must state not only the amount, but also the time This concept—that money today is worth more than the same amount of money in the future—is called the time value of money The present value of an amount... derive the general formula for this process First, the total amount we have at any time is the future value of $1,000 at that time Thus, $1,500 is the future value of $1,000 after 5 years Second, the annual interest rate is called the nominal rate, the quoted rate, or the stated rate Rather than restricting ourselves to annual calculations, we let n measure the total number of interest periods, of which... times per year on the minimum daily balance and credited to the account at the end of the month Helen has an opening balance of $1,000 at the beginning of April On April 11 she deposits $200, and on April 21 she withdraws $300 How much interest does she earn in April? Solution Here i(m) = 0.05 and m = 365, so i = 0.05/365 From April 1 to the end of April 11 Helen has $1,000 in the bank, so the interest... happens to the principal appreciation if we double the number of periods n If we look at the 10% curve in Fig 2.2, then we see that the vertical distance from the future value at n = 20 (about $6.70) to the present value ($1) is more than twice the distance from the future value at n = 10 (about $2.60) to the present value ($1) This suggests that doubling the number of periods more than doubles the principal... 1.1 Future Value of $1 at 5% and 10% simple interest • The quantity (Pn − P0 )/P0 is called the rate of return Notice that in the case of simple interest we have (Pn − P0 )/P0 = ni, so doubling either n, the number of interest periods, or i, the interest rate per period, doubles the rate of return • The quantity (Pn − P0 )/(nP0 ) is the rate of return per period Notice that in the case of simple interest... from the date m1 /d1 /y1 to the date m2 /d2 /y2 , where mi is the number of the month, di the day, and yi the year of the date (i = 1, 2), is given by the formula9 Number of days = 360 (y2 − y1 ) + 30 (m2 − m1 ) + (d2 − d1 ) 8 9 (1.3) Because financial transactions are rounded to the nearest penny, all calculations are subject to roundoff error It makes a difference whether the rounding is done before... convention is said to be computed by the Banker’s Rule 1.3 Problems Walking 1.1 Tom Kendrick invests $1,000 at a nominal rate of i(1) , and he withdraws the interest at the end of each year At the end of the fourth year he has earned $300 in total interest What nominal interest rate does he earn? 1.2 Tom Kendrick invests $1,000 at a nominal rate of i(2) , and he withdraws the interest at the end of each six... months At the end of the fourth year he has earned $300 in total interest What nominal interest rate does he earn? Would you expect it to be higher or lower than the answer to Problem 1.1? 1.3 Hugh Kendrick has a savings account that pays interest at a nominal rate of 3% Interest is calculated 365 times a year on the minimum daily balance and credited to the account at the end of the month Hugh has an opening... between the given dates, excluding either the first or last day Thus, the actual number of days between January 31 and February 5 is 5 Table 1.3 on p 9 numbers the days of a year and is useful when computing the actual number of days Example 1.4 How many actual days are there between May 4, 2005 and October 3, 2005? Solution From Table 1.3, May 4 is day number 124 and October 3 is day number 276 So the. .. calculate the value of an amount of money at a future time—that is, when we calculate the future value from the present value—we talk of compounding When we calculate the value of an amount of money at a previous time—that is, when we calculate the present value from the future value—we talk of discounting For example, if we invest $1,000 at 6% compounded annually for two years, 2 then this $1,000 grows to . class="bi x0 y0 w1 h0" alt="" An Introduction to the Mathematics of Money David Lovelock Marilou Mendel A. Larry Wright An Introduction to the Mathematics of Money Saving and Investing David Lovelock. to the third table in Chapter 1, and Problem 1.5 refers to the fifth problem in Chapter 1. The symbol indicates the end of an example, and the symbol  indicates the end of a proof. Many of the. and lending,andbuying and selling. • borrowing and lending. When you put money into a bank savings account, you are lending your money and the bank is borrowing it. You can lend money to a bank,