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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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Presentation Transcript
basics
Basics
  • Annuities are streams of payments, in our case for a specified length
  • Boil down to geometric series
two main formulas
Two main formulas
  • For annuities due (double dots), simply change denominator from i to d
  • Once again, if unsure make a TIMELINE
deferred annuities
Deferred Annuities
  • Annuity with the whole series of payments pushed back
  • No need to know formulas, just use TVM factors to shift
shortcuts
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
Perpetuities
  • No new formulas, just plug in infinity for n in the originals
  • Interestingly, this leads to
annuities with off payments
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
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
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
Geometric Progression
  • Can usually figure out using geometric series, without any special formulas
calculator highlights
Calculator Highlights
  • Beg/End option
  • Always clear TVM values and check beg/end, compounding, etc options
problems
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

Answer: 324.73

slide13

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

Answer: 12.25%

slide14

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

Answer: .858

slide15

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

Answer: 655.70

slide16

Kathryn deposits $100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i. The accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account at the end of 20 years. Calculate X. ASM p.165

Answer: 6,195

slide17

Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month therafter the payment increases by 2. The nominal interest rate is 9% convertible quarterly. Calculate X. ASM p.205

Answer: 2,729

slide18

A perpetuity-immediate pays 100 per year. Immediately after the fifth payment, the perpetuity is exchanged for a 25-year annuity-immediate that will pay X at the end of the first year. Each subsequent annual payment will be 8% greater than the preceding payment. Immediately after the 10th payment of the 25-year annuity, the annuity will be exchanged for a perpetuity-immediate paying Y per year. The annual effective rate of interest is 8%. Calculate Y. ASM p.228

Answer: 54