【正文】 ∴ A≈ 1萬 () / ≈ 12066 118 年金例解 2 ?某人從銀行貸款 100萬買房， 年利率為6% (.5% = .005 per month)，若在 5年內(nèi)還清，那么他每個(gè)月須還多少錢 ？ ?100萬 = A (P/A, .005, 60) ?100萬 = A [1 – 1/] / .005 ? 5000 = A [1 – 1/] ? 5000 = A [1 – 1/] ? A = 119 Buying a House ?You are ready to buy a house and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000 and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly ine. The interest rate on the loan is 6% per year with monthly pounding (.5% per month) for a 30year fixed rate loan. ?How much money will the bank loan you ? How much can you offer for the house ? 120 Buying a House Continued ?Bank loan ?Monthly ine = 36,000 / 12 = 3,000 ?Maximum payment = .28(3,000) = 840 ?PV = 840[1 – 1/] / .005 = 140,105 ?Total Price ?Closing costs = .04 (140,105) = 5,604 ?Down payment = 20,000 – 5604 = 14,396 ?Total Price = 140,105 + 14,396 = 154,501 121 PV,還是 FV 、年金或混合現(xiàn)金流 解決資金時(shí)間價(jià)值問題的步驟 122 如下現(xiàn)金流，按 10%折現(xiàn) 的 PV 是多少 ？ 混合現(xiàn)金流 Example 0 1 2 3 4 5 $600 $600 $400 $400 $100 PV0 10% 年末 123 現(xiàn)金流 逐個(gè) 折算法 0 1 2 3 4 5 $600 $600 $400 $400 $100 10% $ $ $ $ $ $ = PV0 124 分組年金 (1) 0 1 2 3 4 5 $600 $600 $400 $400 $100 10% $1, $ $ $1, = PV0 [查表如下： ] $600(PVIFA10%,2) = $600() = $1, $400(PVIFA10%,2)(PVIF10%,2) = $400()() = $ $100 (PVIF10%,5) = $100 () = $ 125 分組年金 (2) 0 1 2 3 4 $400 $400 $400 $400 PV0 = $. 0 1 2 $200 $200 0 1 2 3 4 5 $100 $1, $ $ + + 126 例： ?某企業(yè)購買一大型設(shè)備，若貨款 現(xiàn)在 (0年末 ) 一次性付清需 100萬 元；也可采用分期付款，從 第二年年末到第四年年末每年付款 40萬 元。 Years 4 and 5 CFs = $300. The required discount rate is 7% ?What is the value of the cash flows at year 5? ?What is the value of the cash flows today? ?What is the value of the cash flows at year 3 ? 89 Part 6 Annuities and Perpetuities 90 Annuities and Perpetuities ?Annuity – finite series of equal payments that occur at regular intervals ?If each payment occurs at the end of each period, it is called an ordinary annuity ?If each payment occurs at the beginning of each period, it is called an annuity due ?Perpetuity – infinite series of equal payments 91 年金 ?年金： 相等間隔期 （通常為年，但 是也可為其他間隔期，如： 季 、月、每兩年，等） 的 一系列 相同 金額的 收款 或 付款 . 92 年金實(shí)例 ? 學(xué)生貸款償還 ? 汽車貸款償還 ? 保險(xiǎn)金 ? 抵押貸款償還 ? 養(yǎng)老儲蓄 93 年金例 — 解答見后 ?某人現(xiàn)年 51歲，希望在 60歲退休后從 61歲 初 開始的 9年內(nèi)每年年初能從銀行得到 10,000元，那么他在從 52歲初 開始到 60歲 初 的 9年內(nèi)必須每年年初存入銀行多少錢才行 ？ 年利率 6% ?某人從銀行貸款 100萬買房，年利率為 6%，若在 5年內(nèi)還清，那么他每個(gè)月必須還多少錢才行？ 94 ?普通年金 : 若所求終值的時(shí)刻為 最后一筆年金 所在的時(shí)刻， or 所求現(xiàn)值的時(shí)刻為 第一筆年金 所在的時(shí)刻的 前 1期 ，則稱該年金為 普通年金 求 該年金的現(xiàn)值 or終值可查 普通年金 現(xiàn)值 or終值 因子表 。 ?由此可見，該促銷僅能給你 $l00 = $。 這項(xiàng)投資到今天 會值 多少錢呢 ? ?該復(fù)利終值因子為： (1+ r)377 = ? 11,038 42 Effects of Compounding – 小結(jié) ?The effect of pounding is small for a low interest rate, and for a small number of periods. ?For a given interest rate – the longer the time period, the bigger the future value. ?For a given time period – the higher the interest rate, the bigger the future value. 43 Figure : $1于不同利率、多期后的復(fù)利終值 44 $1,000 按 12% 復(fù)利，需要多久成為 $2,000 (近似 ) ? 想使自己的財(cái)富倍增嗎 ! 快捷計(jì)算方法 : 72 法則 45 近似 . N = 72 / i% 72 / 12% = 6 年 [精確計(jì)算是 年 ] 快捷計(jì)算方法： 72法則 $1,000 按 12% 復(fù)利，需要多久成為 $2,000 (近似 ) ? 46 Quick Quiz: Part 1 ?What is the difference between simple interest and pound interest ? ?Suppose you have $500 to invest and you believe that you can earn 6% per year over the next 12 years. ?How much would you have at the end of 12 years using simple interest ? ?How much would you have at the end of 12 years with pound interest ? 47 Part 2 Present Value and Discounting 48 Present Values ?How much do I have to invest today to have some amount in the future? ?FV = PV(1 + r)t ?Rearrange to solve for PV = FV / (1 + r)t ?When we talk about discounting, we mean finding the present value of some future amount. ?When we talk about the “value” of someth., we are talking about the present value unless we specifically indicate that we want the future value. 49 假設(shè) 2 年 后你需要 $1,000. 那么按 7%復(fù)利，你現(xiàn)在要存多少錢 ？ 0 1 2 $1,000 7% PV1 PV0 復(fù)利現(xiàn)值 50 PV0 = FV2 / (1+r)2 = $1,000 / ()2 = FV2 / (1+r)2 = $ 復(fù)利現(xiàn)值公式 0 1 2 $1,000 7% PV0 51 PV0 = FV1 / (1+r)1 = FV1(1+r)1 PV0 = FV2 / (1+r)2 = FV2(1+r)2 P V 公式 : PV0 = FV n / (1+r)n = FV n (1+r)n or PV0 = FV n (PVIF r,n) 見下頁表格 (PVIF r,n) 可直觀地記為 (PV/FV, r , n) 一般復(fù)利現(xiàn)值公式 etc. 52 PVIF r,n表如下所示： 復(fù)利現(xiàn)值因子表： PVIF r,n 期限 6% 7% 8% 1 .943 .935 .926 2 .890 .873 .857 3 .840 .816 .794 4 .792 .763 .735 5 .747 .713 .681 53 PV2 = $1,000 (PVIF7%,2) = $1,000 (.873) = $873 [四舍五入 ] 查復(fù)利現(xiàn)值因子表 期限 6% 7% 8% 1 .943 .935 .926 2 .890 .873 .857 3 .840 .816 .794 4 .792 .763 .735 5 .747 .713 .681 54 按 10% 的復(fù)利折算， 5 年 后的 $1,000 的現(xiàn)值是多少？ Example 復(fù)利現(xiàn)值 0 1 2 3 4 5 $1,000 PV0 10% 55 ? 用公式 : PV0 = FV n / (1+r)n PV0 = $1,000 / (1+ )5 = $620. 92 ? 查表 : PV0 = $1,000 (PVIF10%, 5) = $1,000 (.621) = $621. 00 [四舍五入 ] 解： 5