期初年金：指在一定时期内，以相同的时间间隔在各期期初收入或支出的 等额的款项。
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4.4.1 HOW TO VALUE PERPETUITIES如何计算永 续年金
Suppose that you could invest $100 at an interest rate of 10%. You would earn annual interest of .10 × $100 = $10 per year and could withdraw this amount from your investment account each year without ever running down your balance. 初始投资为$100年利率为10%的 投资可使投资者每年支取$10的利息而不会减少账户资金。
CHAPTER 4
THE TIME VALUE OF MONEY 资金的时间价值
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定义：
CO与复利 COMPOUND INTEREST
Suppose you have $100 invested in a bank account, interest rate of 6% per year 假设银行账户中有100刀，年利率为6%
Interest in year 1 = .06 ×$100 = $6 Value of investment after 1 year = $100+$6 = $106
Present value = future value/l.06 = $100
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In general, for a future value or payment t periods away 公式化之后：现值即等于终值除以终值系数 Present value = future value after t periods/(1+r)t
The calculation is therefore termed a discounted cash flow (DCF贴现现金流) calculation, an the interest rate r is known as the discounted rate。利率r即是贴现率。 (P96.)
You might be able to put $1200 in the bank, a second deposit of $1400 in 1 year in 2 years. 两年内存了三笔，第一笔$1200，第二笔$1400，第三笔$1000，假 设都是年初存入。
If you earn an 8% rate of interest. How much be available to spend 2 years from now? 若年利率为8%，复利计算，那么三年后可用资金额是多少？
4. Level cash flows: perpetuities and annuities 水平现金流：永续年金和年金 5. Inflation and the time value of money通胀与资金的时间价 值 6. Effective annual interest rates有效年利率
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The present value of a stream of future cash flows is the amount you need to invest today to generate that stream. To find the PV, you just calculate the PV of each flow and then add them. 计算多笔未来现金流量的现值，只需分别计算出每笔现金流的现 值，然后加总即可。
Present value (PV): value today of a future cash flow
现值：未来一定时间特定资金的现在价值。(P95.)
To calculate present value, we discounted the future value at the interest rate r. 为了计算现值，我们按利率r将未来价值贴现。
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4.3.2 PRESENT VALUE OF MULTIPLE CASH FLOWS 多笔现金流的现值
Suppose your auto dealer gives you a choice between paying $15500 for a new car or entering into an installment plan where you pay $8000 down today and make payments of $4000 in each of the next 2 years. Assume that the interest rate you can earn on safe investments is 8%. 假设你有一个购车计划，可以选择一次性支付$15500，或者 分期付款——首付$8000，之后的两年每年支付$4000，无风 险投资收益率为8%。你会如何选择？ Which is the better deal?
Obviously, the higher the rate of interest, the faster your savings will grow with years.
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An example of a future value table, showing how an investment of $1 grows with compound interest
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Present value of a future cash flow of $100
The longer, the less it is worth today 支付期限越长，现在所需的 初始投资额越少。
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An example of present value table, showing the value today of $1 received in the future. 未来特定时间的1美元的现值：
FV factor终值系数 = (1+r)t
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4.2 PV现值
$100 invested for 1 year at 6% will grow to 本金$100，投资期1年，利息6%，终值(FV)为 $106= (100×1.06) How much we need to invest now in order to produce $106 at the end of the year? 反之，若想在一年后获得$106，那么初始投资金额 应为多少呢？
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本章导读
• 公司需要筹集资金（raise funds）以支付投资，并因 此承担了在未来时点还款的责任；个人也可能通过借 贷（student loan）获得大学教育所需资金，并计划 在未来用工资收入偿债。
• 因此所有的财务决策（financial decision）都必须对 不同时点的现金流量（cash flows）进行比较。 • 本章首先分析了按特定利率（given interest rate）进
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Simple interest单利：the interest only on your original investment. 在贷款期间只就本金计算利息，利息不再加入 本金计算利息。(P92.)
How an investment of $100 grows with compound interest at different interest rate 本金为$100的投资不同利率水平下的复利增长
货币的时间价值就是指当前所持有的一定 量货币比未来获得的等量货币具有更高的 价值。从经济学的角度而言，现在的一单 位货币与未来的一单位货币的购买力之所 以不同，是因为要节省现在的一单位货币 不消费而改在未来消费，则在未来消费时 必须有大于一单位的货币可供消费，作为 弥补延迟消费的贴水。
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$15133.06 < 15500 The installment plan is preferable
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4.4 level cash flows水平现金流
•Annuity: equally spaced level stream of cash flows, with a finite maturity
For an interest rate of r and a horizon of t years, 一笔时限为t年利率为r的初始金额为$100的投资的终值：
Future value of $100 = $100×(1+r)t
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Compound interest: interest earned on interest 复利：利滚利（将所生利息计 入本金再计利息）( P92).
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To find the value at some future date of a stream of cash flows, calculate what each flow will be worth at that future date, and then add up these future values. 计算多笔现金流的终值，只需分别计算单笔现金流的终 值，然后加总即可。