英文版公司理财课件chapter 4

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Future-values are typically measured at the end of a project’s life, while presentvalues are measured at the start of a project’s life (time zero).
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Suppose you have $100 invested in a bank account, interest rate of 6% per year
Interest in year 1 = .06 ×$100 = $6 Value of investment after 1 year = $100+$6 = $106
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example
If you invest $10 000 at an 8% annual return until age 65, the table below shows how much you would get back
Age when you started the $10 000 investment 20yrs $319 204 30yrs $147 853 40yrs $68 485 50yrs $31 722
The table gives the value of FVIF=(1+r)t ,which is indexed of a given interest rate, r, and a specified period of time, t The future-value interest factor for a single amount is always greater than one By multiplying the interest factor from the table for the future value of one dollar by the present amount, the future amount can be found The interest factor for the future value of one dollar increase as both interest rate and time increase
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If you start investing now, time can be a very powerful ally. Year after year, the money you invest earns more money. And if you reinvest your earnings, you can earn even more money in the future, it’s called compounding returns and its one of the keys to making your money work harder.
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ቤተ መጻሕፍቲ ባይዱ
The table compares the growth of $100 invested at compound versus simple interest. Notice that in the simple interest case, the interest is paid only on the initial investment of $100.
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Compound interest: interest earned on interest
Simple interest
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There is an important distinction between compound interest and simple interest. When money is invested at compound interest, each interest payment is reinvested to earn more interest (earn interest on interest ) in subsequent periods. In contrast, the opportunity to earn interest on interest is not provided by an investment that pays only simple interest.
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Content
Future values and compound interest Present values Multiple cash flows Level cash flows: perpetuities and annuities Inflation and the time value of money Effective annual interest rates
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An example of a future value table, showing how an investment of $1 grows with compound interest
FV factor = (1+r)t
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A table of interest factors for the future value of one dollar deposited at the start of the year can used to simplify compound interest calculations.
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The equation for future value :
future value : F = P ·（ 1+r）n
（1+r）n——future value interest factor for an initial principal of $1 compounded at r per cent for n periods, using （F/p，r，n ）。 。 F: future value at the end of period n P: initial principal, or present value r: annual rate of interest paid n: number of periods (typically years)
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Problem
Daniel Busch will deposit $3000 today into an account paying interest of 12 per cent, compounded annually, and leave his money on deposit for three years, how much will he have?
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Future value: 终值、未来价值 Compound interest: 复利 Simple interest: 单利
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Time line, which is a horizontal line on which time zero is at the left-hand end and future periods are shown as you move from left to right, can be used to depict the cash flows associated with a given investment. The negative values representing cash outflows and the positive values representing cash inflows.
Interest in year 2 = .06 ×$106 = $6.36 Value of investment after 1 year = $106+$6.36 = $112.36
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Future value: amount to which an investment will grow after earning interest For an interest rate of r and a horizon of t years, Future value of $100 = $100×(1+r)t
Chapter 4
The time value of money
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In this chapter you will gain an understanding of the important time-value concepts and mathematics that are widely used in the financial decision-making process and are employed in later chapters.
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For compounding to work its magic, you need to do two things:
1. Reinvest your investment returns (e.g. dividends and interest), rather than spending the money on other things. This will enable you to turn your investment earnings into capital so that you can generate even more future earnings. An easy way to reinvest income is to participate in a dividend, interest or income reinvestment scheme.
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For compounding to work its magic, you need to do two things:
2. Give your investment time to grow by starting your investment as soon as possible and keep it going for as long as you can .
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How an investment of $100 grows with compound interest at different interest rate
The higher the rate of interest, the higher the future value, and the longer the period of time, the higher the future value
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Objectives
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Calculate the future value to which money invested at a given interest rate will grow Calculate the present value of a future payment Calculate present and future values of a series of cash payments Find the interest rate implied by present and future values Understand the difference between real and nominal cash flows and between real and nominal interest rates. Compare interest rates quoted over different time intervals—for example, monthly versus annual rates.