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Financial Mathematics Old FM Forum 

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#1




Done with the exam? Share your Exam 2/FM study notes here!
You can post your notes online using the upload button after clicking post reply, or you can always email them to me at tom(at)actuarialoutpost.com. If that isn't easy enough, just PM me here and I can send you my fax number or we can work something else out!
Any questions about what/how to post, can be answered here! Thanks! ===================== \\\\\\\ please read /////// ===================== All posts in this thread that do not have notes attached will be deleted! Members who donate notes* will be added to a user group much like the site supporters. This group will have added privileges such as a larger avatar and a custom user title other than 'member.' Please note that some notes may be out of date, contain information that may no longer be tested, or not cover all required information for your exam. Please check your exam syllabus for a list of required study topics for your exam, before using these notes. Notes that have been donated have not been checked for accuracy! If you do find an error in any of the notes, please feel free to point them out to me (or the original poster) via PM and I can edit the post where they were uploaded to call the error to everyone's attention. Please only post notes that you own or have permission to post. Please respect other’s intellectual property and only post notes that meet our copyright policy. Thanks again, Tom *a respectable amount ===================== /////// please read \\\\\\\ ===================== 
#3




wow!
Thank you so much for posting these notes! I've been using them 1) to look up formulas I've forgotten when I'm studying at work (since my books are at home) and 2) to get specific information that differs from Broverman (such as GICs), since I don't have the Kellison book. You rock

#4




FM Formulas
NEW PRINTABLE VERSION!
Scroll down to the bottom for a PDF that prints nicely. I will leave the original post up here so that folks can use it as a quick reference. no driver 11/12/2006 Introduction: Since ASM does not have a formula summary, I decided to compile one to use as I started working on old test questions. In the interest of other actuarial students, I thought I would share the results. A few notes:
no driver 10/08/2006 Chapter 1: Basics: : accumulation function. Measures the amount in a fund with an investment of 1 at time 0 at the end of year . : amount of growth in year . : rate of growth in year , also known as the effective rate of interest in year . : any accumulation function can be multiplied by a constant (usually the principal amount invested) to obtain a result specific to the amount invested. Common Accumulation Functions: : simple interest. : variable interest. : compound interest. Present Value and Discounting: : amount you must invest at time 0 to get 1 at time . : effective rate of discount in year . Some Useful Relationships: Nominal Interest and Discount: and are the symbols for nominal rates of interest compounded mthly. Force of Interest: : definition of force of interest. If the Force of Interest is Constant: Chapter 3: Annuities: : PV of an annuityimmediate. : PV of an annuitydue. : AV of an annuityimmediate (on the date of the last deposit). : AV of an annuitydue (one period after the date of the last deposit). Perpetuities: : PV of a perpetuityimmediate. : PV of a perpetuitydue. Chapter 4: mthly Annuities & Perpetuities: : PV of an nyear annuityimmediate of 1 per year payable in mthly installments. : PV of an nyear annuitydue of 1 per year payable in mthly installments. : AV of an nyear annuityimmediate of 1 per year payable in mthly installments. : AV of an nyear annuitydue of 1 per year payable in mthly installments. : PV of a perpetuityimmediate of 1 per year payable in mthly installments. : PV of a perpetuitydue of 1 per year payable in mthly installments. Continuous Annuities: Since , : PV of an annuity (immediate or due) of 1 per year paid continuously. Payments in Arithmetic Progression: In general, the PV of a series of payments, where the first payment is and each additional payment increases by can be represented by: Similarly: : AV of a series of payments, where the first payment is and each additional payment increases by . : PV of an annuityimmediate with first payment 1 and each additional payment increasing by 1; substitute for in denominator to get due form. : AV of an annuityimmediate with first payment 1 and each additional payment increasing by 1; substitute for in denominator to get due form. : PV of an annuityimmediate with first payment and each additional payment decreasing by 1; substitute for in denominator to get due form. : AV of an annuityimmediate with first payment and each additional payment decreasing by 1; substitute for in denominator to get due form. : PV of a perpetuityimmediate with first payment 1 and each additional payment increasing by 1. : PV of a perpetuitydue with first payment 1 and each additional payment increasing by 1. Additional Useful Results: : PV of a perpetuityimmediate with first payment and each additional payment increasing by . : PV of an annuityimmediate with mthly payments of in the first year and each additional year increasing until there are mthly payments of in the nth year. May God Have Mercy on Your Soul: : PV of an annuityimmediate with payments of at the end of the first mth of the first year, at the end of the second mth of the first year, and each additional payment increasing until there is a payment of at the end of the last mth of the nth year. : PV of an annuity with continuous payments that are continuously increasing. Annual rate of payment is at time . : PV of an annuity with a continuously variable rate of payments and a constant interest rate. : PV of an annuity with a continuously variable rate of payment and a continuously variable rate of interest. Payments in Geometric Progression: : PV of an annuityimmediate with an initial payment of 1 and each additional payment increasing by a factor of . Chapter 5: Definitions: : payment at time . A negative value is an investment and a positive value is a return. : PV of a cash flow at interest rate . Chapter 6: General Definitions: : payment made at the end of year , split into the interest and the principle repaid . : interest paid at the end of year . : principle repaid at the end of year . : balance remaining at the end of year , just after payment is made. On a Loan Being Paid with Level Payments: : interest paid at the end of year on a loan of . : principle repaid at the end of year on a loan of . : balance remaining at the end of year on a loan of , just after payment is made. For a loan of , level payments of will pay off the loan in years. In this case, multiply , , and by , ie etc. Sinking Funds: : total yearly payment with the sinking fund method, where is the interest paid to the lender and is the deposit into the sinking fund that will accumulate to in years. is the interest rate for the loan and is the interest rate that the sinking fund earns. Chapter 7: Definitions: : Price paid for a bond. : Par/face value of a bond. : Redemption value of a bond. : coupon rate for a bond. : modified coupon rate. : yield rate on a bond. : PV of . : number of coupon payments. : base amount of a bond. Determination of Bond Prices: : price paid for a bond to yield . : Premium/Discount formula for the price of a bond. : premium paid for a bond if . : discount paid for a bond if . Bond Amortization: When a bond is purchased at a premium or discount the difference between the price paid and the redemption value can be amortized over the remaining term of the bond. Using the terms from chapter 6: : coupon payment. : interest earned from the coupon payment. : adjustment amount for amortization of premium ("write down") or : adjustment amount for accumulation of discount ("write up"). : book value of bond after adjustment from the most recent coupon paid. Price Between Coupon Dates: For a bond sold at time after the coupon payment at time and before the coupon payment at time : : "flat price" of the bond, ie the money that actually exchanges hands on the sale of the bond. : "market price" of the bond, ie the price quoted in a financial newspaper. Approximations of Yield Rates on a Bond: : Bond Salesman's Method. Price of Other Securities: : price of a perpetual bond or preferred stock. : theoretical price of a stock that is expected to return a dividend of with each subsequent dividend increasing by , . Chapter 9: Recognition of Inflation: : real rate of interest, where is the effective rate of interest and is the rate of inflation. Method of Equated Time and (Macauley) Duration: : method of equated time. : (Macauley) duration. Volatility and Modified Duration: : PV of a cash flow at interest rate . : volatility/modified duration. : alternate definition of (Macauley) duration. Convexity and (Redington) Immunization: convexity To achieve Redington immunization we want: Download this formula summary: Prints nicer than this post too. Last edited by no driver; 11142006 at 04:02 PM.. 
#7




Thank you for sharing.

#8




thx for this nice and long summary, no driver... amazingly i recognize and remember most of those formulas, doing tons of questinos really do help : D

#9




Using the BAII Plus workbook to calculate duration and convexity
The following is an outline of how the BA II plus calculator workbook can be used to calculate the Macaully Duration, Modified Duration and Convexity of a bond for short duration bonds quite easily. I will use the question below to help illustrate: 
Quote:
The following letters are assigned for calculations:  m = coupon frequency/year r = annual effective interest rateCalculating the price
Quote:
Modified Duration Quote:
Quote:
Credit: Credit where credit is due. I learned this method using Yufeng Guo's awesome manual for FM.
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Spoiler: Last edited by Buzz Lightyear; 10282006 at 08:22 PM.. 
#10




Have you tried the question below using the formula shown above?
http://www.math.ilstu.edu/krzysio/KOFMExercise4.pdf 
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