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1、(8) 统 计 与 金 融首 先 用 with命 令 载 入 工 具 包 stats、 finance。 restart; with(stats); with(finance);金 融 工 具 包 （ 本 工 具 包 内 容 未 做 汉 化 ）The finance package assists you in performing financial calculations. With it, you can calculate the present value and accumulated value of annuities, growing annuities, perpetui
2、ties, growing perpetuities and level coupon bonds. Moreover, it can alsohelp you compute the yield to maturity of a bond. You can construct an amortization table, determine the effective rate of interest for a given compound interest rate, and find the present value and future value of a fixed quant
3、ity for a givencompound interest rate.Note: all examples use dollars ($) and interest rates are in terms of percent (%). Moreover, the default setting for floating point precision is 10. Round up each answer that Maple finds to the nearest cent.Amortization MethodThe most common method of repaying i
4、nterest-bearing loans is the amortization method . This procedure is used to liquidate an interest-bearing debt by a seriesof periodic payments, usually equal, at a given interest rate. You may use Maple todetermine how many payments are required to pay off the loan, using the amortization command.
5、You can also create amortization tables.A debt of $100 with interest at 10% per annum is to be amortized by payments of$50 at the end of each year for as long as necessary. A:= amortization( 100, 50, 0.10 );The output from the command above is summarized in the table below. From the result we see th
6、at you must make three payments: $50, $50 and $17.60. The last result in the output, $17.60, is the cost of the loan . amortization_tablen, Payment, Interest, Principal, Balance = matrix(A1);The first column of the matrix refers to the payment number. The second column shows the payment per time per
7、iod. The third column is how much of the payment goes towards paying off the interest. The fourth refers to how much goes to pay off theprincipal per payment. The last column is the outstanding balance of the debt.AnnuitiesMaple can find the present value of ordinary simple annuities.Suppose you wan
8、t to find the present value of an annuity paying $100 per annum,for 5 years, starting in 1 year from now, at an annual interest rate of 10 %. annuity( 100, 0.10, 5 );Consider a growing (increasing) annuity that pays $100 at the end of the first year, then grows at 5 % per annum. It is a five-year an
9、nuity and the annual rateof interest is 10%. Use the growingannuity command. growingannuity( 100, 0.1, 0.05, 5 );If the interest rate changes to % and the growth rate is unknown (call it ), then the future value is given by the formula below. growingannuity( 100, 0.1/12, g, 5*12 );As a final example
10、, analyze the case where the payments per time period are notfixed. Suppose you want to find the present value of variable revenues expectedfrom a project. At the end of year one, the project expects $200 in revenue, and $150 and$100 in years two and three respectively. The opportunity cost of capit
11、al is 7.8%. cashflows( 200, 150, 100, 0.078 );You may generalize the above result. If the discount rate is %, the present value of the benefits earned from the project is given by the cashflows command. cashflows( 200, 150, 100, r );BondsWhen a corporation or government needs to borrow a large sum o
12、f money for a reasonably long period of time, they issue bonds which they sell to investors.A $1000 bond that pays interest at % (bond rate) is redeemable at par at the end of five years. Suppose you want to find the purchase price of the bond to yield an investor 14% compounded semi-annually. (Note
13、: the yield rate always comes before thecoupon rate). levelcoupon( 1000, .14/2, .10/2, 5*2 );The result shows that the bond is purchased at a discount , since the opportunity cost of capital is higher than the bond rate.Suppose you want to find the yield rate to maturity of a bond. Suppose a large c
14、orporation issues a 15-year bond that has a face value of $10 000 000, and paysinterest at a rate of %. If the purchase price of the bond is $11 729 203.32, the yield tomaturity for the bond is found by the yieldtomaturity command. yieldtomaturity( 11729203.32, 10000000.00, .10/2, 30 );That is, appr
15、oximately 4% per half-year, or % .Effective Interest RatesFor a given nominal rate of interest compounded times per year, the annual effective rate of interest is the rate j which, if compounded annually, will produce the same amount of interest per year.Compute the annual effective rate of interest to %effectiverate( .1325, 365 );The annual effective rate works out to be about 14.17%.The effective annual rate of interest corresponding to % is calculated as follows. effectiverate( r, m );As another examp
