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Annuity Equations

  1. Annuity-Immediate

    Pays $5 at the end of each year
    Annual eff. int rate of 4%
    Pays for 8 years
    Find PVo
    PVo= 5(1-(1.04)⁻⁸) / 0.04)
  2. Annuity-Immediate

    Pays $5 at the end of each year
    Annual eff. int rate of 4%
    Pays for 8 years
    Find AV8
    AV8= 5((1.04)⁸ - 1) / 0.04)
  3. Perpetuity-Immediate

    Pay $5 at the end of each year
    Annual eff. int rate of 6%
    Pays forever
    Find PVo
    PVo= 5(1 / 0.06)
  4. Annuity-Due

    Pays $5 at the beginning of each year
    Annual eff. int rate of 4%
    Pays for 8 years
    Find PVo
    PVo= 5(1 - (1/1.04)⁻⁸) / (0.04 / 1.04)
  5. Annuity-Due

    Pays $5 at the beginning of each year
    Annual eff. int rate of 4%
    Pays for 8 years
    Find AVt
    Av8= 5((1.04)⁸ - 1 / 0.04)
  6. Perpetuity-Due

    Pays $5 at the beginning of each year
    Annual eff. int rate of 6%
    Pays forever
    Find PVo
    PVo= 5(1.06 / 0.06)
  7. Deferred Annuity-Immediate

    Pays $1000/yr
    Annual eff. int rate is 6%
    Pays for 15 yrs
    Deferral period of 5 yrs (=k)
    Find PVo
    PVo= 1000(1.06)⁻⁵*(1 - (1.06)¹⁵ / 0.06)
  8. Deferred Annuity-Immediate

    Pays $100/month
    Monthly eff. int rate is 9%
    Pays for 10 years
    Deferral period of 3 years (=k)
    Find PVo
    i¹²= 9% → 0.09/12 = 0.0075

    PVo= 100(1.0075)⁻³ * (1 - (1.0075)¹⁰ / 0.0075)
  9. Deferred Perpetuity-Immediate

    Pays $100/month 
    Monthly eff. int rate is 9%
    Pays forever
    Deferral period of 3 yrs
    Find PVo
    i¹²= 9% → 0.09/12 = 0.0075

    PVo= 100(1.0075)³⁶ * (1/0.0075)
  10. Deferred Annuity-Due

    Pays $300/quarter
    Quarterly eff. int rate is 8%
    Pays for 15 years
    Deferral period of 5 years
    Find PVo
    • i⁴= 8% → 0.08/4= 0.02
    • k= 5 yrs → 20 qrts and n= 15 yrs → 60 qrts
    • d= i/(1+i) → 0.02/1.02= 0.01960

    PVo= 300(1.02)⁻²⁰ * (1 - (1.02)⁶⁰ / 0.01960)
  11. Annuity-Immediate-Paid in Monthly Increments

    Pays $36/yr
    Monthly eff. int rate is 12%
    Paid in monthly increments for 10 years
    Find PVo
    PVo= 36(1 - (1.01)⁻¹⁰*¹² / 0.12)
  12. Perpetuity-Immediate-Paid In Monthly Increments Forever

    Pays $36/yr
    Monthly eff. int rate is 12%
    Paid in monthly increments for 10 years
    Find PVo
    PVo= 36(1/0.12)
  13. Annuity-Due-Paid In Monthly Increments

    Pays $36/yr
    Monthly eff. int. rate of 12%
    Paid in monthly increments for 10 years
    Find AV10
    • i¹²= 12% → 0.12/12= 0.01
    • d¹²= 12[1-(1.01)⁻¹]= 0.1188

    AV10= 36((1.01)¹⁰*¹² - 1) / 0.1188
  14. Continuously Payable Annuity

    Pays $36/yr monthly eff. int rate of 12%
    Makes continuously pmts for 10 years
    Find PVo
    • i¹²= 12% → 0.12/12= 0.01
    • r= 12ln(1.01)= 0.1194

    PVo= 36(1 - (1.01)⁻¹⁰*¹² / 0.1194)
Author
GoBroncos
ID
365909
Card Set
Annuity Equations
Description
Updated

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