2c147a21-4fd2-44d6-9f17-440e603ab8e5 50 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

The Financial Modeling package is a collection of tools for mathematical finance. This package builds on the functionality available in other packages such as LinearAlgebra, Statistics, Optimization, and CurveFitting. The package supports a wide range of common tasks such as date arithmetic, cash flow analysis, option pricing, term structure analysis, and simulation.

growingperpetuity computes the present value of a perpetuity paying the amount cash one period from now, with increasing payments at the end of each periods. The payments increase according to the growth rate. finance[growingperpetuity](1.5,0.11,0.2) parse maple 16.66666667 -

<should be positive

Levelcoupon calculates the present value at interest rate rate of a bond with face value face maturing in maturity period and paying at a rate couponrate per period.   The coupon rate is the rate that determines the payments that the bond gives. The rate is the interest rate used in calculating the present value of the bond. finance[levelcoupon]((1000, 0.10/2,  0.12/2, 6)) parse maple 1050.756921

finance[levelcoupon]((1000, 0.12/2, 0.12/2, 6)) parse maple 999.9999998

finance[levelcoupon](1000, 0.14/2, 0.12/2, 6) parse maple 952.3346034

growingannuity calculates the present value at period=0, of an annuity of nperiods payments, starting at period=1 with a payment of cash. The payments increase at a rate growth per period. finance[growingannuity](100,0.11,0.03,5) parse maple 390.0340764

futurevalue function carries an amount towards the future; the presentvalue function carries it towards the past. finance[futurevalue](1000, 0.06, 3) parse maple 1191.016

10001 0.06 + (3^* 1191.016

blackscholes computes the present value of an European call option without dividends under Black-Scholes model.•      The function requires the value of the standard deviation. It can be calculated from the variance by taking the square root.•      The hedge ratio is the ratio of the expected stock price at expiration to the current stock price.•      There are strong assumptions on the Black-Scholes model. Use at your own risk. Refer to appropriate finance books for the list of assumptions. evalf(finance[blackscholes](50.00, 49.00, 0.07, 199/365, sqrt(0.09))) parse maple 5.849179521

See what happens if the stock price increases: evalf(finance[blackscholes](50.00+1.00, 49.00, 0.07, 199/365, sqrt(0.09))) parse maple 6.511555004

presentvalue gives the value at period=0 of an amount given at period=nperiods. The interest rate is given by rate.•      The present value concept is arguably the most important concept behind the personal finance portion of the Finance package. It allows one to properly account for the time value of money.                                 # I will require 100 U in three years. I will receive 12% per year at the bank.# How much much should I deposit now so that I obtain the appropriate amount in# 3 years? evalf(finance[presentvalue](100, .12, 3)) parse maple 71.17802478

^This works to 8 decimal points, but Smath (below) to 15...

1001 0.12 + (3^/ 71.1780247813411

A given loan is at 12% compounded monthly. The effective rate is then 1% monthly compounded 12 times. One can calculate it as follows: finance[effectiverate](0.12,12) parse maple 0.12682503

^This works to 8 decimal points, but Smath (below) to 15...

1 0.12 12 / + (12^1 - 0.12682503013197

amortization command gives a sequence of two elements: an amortization table and the cost of the loan.•      The amortization table consists of lists:                                                                1) The period number2) The amount of the payment3) The interest for the period finance[amortization](1000.00, 500.00, 0.10) parse maple [[0 001000 - 1000.00] [1 500100400 600.0000] [2 50060440 160.000000] [3 17616160 0]] 17621 mat

annuity gives the present value at time=0 of an annuity of nperiods equal payments of the amount cash, starting at time=1.•      Mortgages are examples of annuities. finance[annuity](100,0.10,15) parse maple 760.6079506

perpetuity computes the present value of an instrument that pays the amount cash at the beginning of each period, forever, starting in one period.•      An example of a perpetuity is a stock that pays the same dividends year after year. finance[perpetuity](1.5,0.11) parse maple 13.63636364

Utility ABC pays a dividend of 1.5 units per share every year. Given a discount rate of 11%, what is the present value per share of those dividends?

yieldtomaturity the interest rate rate of a bond with face value face, present value amount, maturing in maturity period and paying at a rate couponrate per period.•      The coupon rate is the rate that determines the payments that the bond gives. finance[yieldtomaturity](1050.75,1000,0.12/2,6) parse maple .5000132125e 1 -

cashflows computes the present value of a list of cash flows. The flows are given one per period, starting at period 1. finance[cashflows](( [100, 200, 50], 0.1 )) parse maple 293.7640872

If these cash flows are generated from an initial investment of 95 units, the net present value is

95 - finance[cashflows](( [100, 200, 50], 0.1 )) parse maple + 198.7640872

References : Maple Tools.log and https://www.maplesoft.com/support/help/Maple/view.aspx?path=Finance/cashflows&cid=330