Exam FM/2 Review Annuities

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# Exam FM/2 Review Annuities - PowerPoint PPT Presentation

Exam FM/2 Review Annuities. Basics. Annuities are streams of payments, in our case for a specified length Boil down to geometric series. Two main formulas. For annuities due (double dots), simply change denominator from i to d Once again, if unsure make a TIMELINE. Deferred Annuities.

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### Exam FM/2 ReviewAnnuities

Basics
• Annuities are streams of payments, in our case for a specified length
• Boil down to geometric series
Two main formulas
• For annuities due (double dots), simply change denominator from i to d
• Once again, if unsure make a TIMELINE
Deferred Annuities
• Annuity with the whole series of payments pushed back
• No need to know formulas, just use TVM factors to shift
Shortcuts
• Block Payments
• Show graph
• For PV, start with last payment and move back to time 0
• For AV, start with first payment and move forward to end
• Just an example of manipulating annuities
• Prove algebraically (SS) or logically as deferred plus immediate
• Another example of manipulating annuities
Perpetuities
• No new formulas, just plug in infinity for n in the originals
Annuities with off payments
• 1st method- Find equivalent interest rate for payment period
• This is the easiest/quickest, so use this if possible
• 2nd Method- More complicated, but may have to use if you are only given symbols
• Multiple payments during interest pd- mthly annuity
• Mthly annuity- divide by # payments and use i^(m)
• Multiple interest pds per payment- split up payments (show)
More Annuities
• If payable continuously, continue pattern and change i to δ
• Double dots and upper m’s cancel
• If payments vary continuously and/or interest varies continuously (unlikely)
Arithmetic progression
• General formula- annuity of first payment plus increasing annuity of the common difference
• This leads to 3 other forms by bringing through time (show)
• From these, you can derive all 4 increasing/decreasing formulas (show)
Geometric Progression
• Can usually figure out using geometric series, without any special formulas
Calculator Highlights
• Beg/End option
• Always clear TVM values and check beg/end, compounding, etc options
Problems
• A man turns 40 today and wishes to provide supplemental retirement income of 3000 at the beginning of each month starting on his 65th birthday. Starting today, he makes monthly contributions of X to a fund for 25 years. The fund earns a nominal rate of 8% compounded monthly. Each 1000 will provide for 9.65 of income at the beginning of each month on his 65th birthday until the end of his life.Calculate X.
• ASM p.109

To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years.The annual effective rate of interest is i. You are given (1+i)^n=2.0Determine i. ASM pg. 123

Dottie receives payments of X at the end of each year for n years. The present value of her annuity is 493.Sam receives payments of 3X at the end of each year for 2n years. The present value of his annuity is 2748.Both present values are calculated at the same annual effective interest rate.Determine v^n. ASM p.136

A loan of 10,000 is to be amortized in 10 annual payments beginning 6 months after the date of the loan. The first payment, X, is half as large as the other payments. Interest is calculated at an annual effective rate of 5% for the first 4.5 years and 5% thereafter. Determine X. ASM p.153