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The annual eff. int rate is 4%. An annuity-immed. makes pmts of $5 at the end of each year for 8 years. Find the PV of the annuity-immed.
- PVo= 5v + 5v² + 5v³+...+5v⁸
- = 5(v+v²+...+v⁸)
- = 5a_8|4%
- = 5(1-v⁸/i)
- = 5 ((1-1.04)-⁸) / 0.04
- = 33.66
- OR, use calculator
- 8[N]4[I/Y]5[PMT][CPT][PV]
- = -33.66, then make positive
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The annual eff. int rate is 4%. An annuity-immed makes level pmts at the end of each year for 8 years. The PVo of the annuity-immed 33.6637. Calculate the amount of each level pmt.
- PVo= (Pmt) a_8|4%
- 33.6637 = (Pmt) ((1-1.04)-⁸) / 0.04
- 33.6637 = (Pmt) 6.7275
- Pmt= 5.00
- OR, use calculator
- 8[N]4[I/Y]33.6637[PMT][CPT][PMT]
- =-5.00, then make positive
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The annual eff. int rate is 4%. An annuity-immed. makes pmts of $5 at the end of each year for 8 years. Calculate the accumulated value of the annuity-immed. at the end of 8 years.
- AV₈= 5(1.04)⁷+5(1.04)⁶+...+5(1.04)+5
- = 5 * (1.04⁸-1) / 0.04
- = 5*(9.2142)
- = 46.07
- OR, use calculator
- 8[N]4[I/Y]5[PMT][CPT][FV]
- = -46.07, then make positive
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The annual eff. int rate is 6%. A perpetuity-immed. makes pmts of $5 at the end of each year forever. Calculate the PV of the perpetuity-immed.
- PVo= 5a_∞|
- = 5(1/0.06)
- = 83.33
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True of False?
1) a_n = vä_n
b) ä_n+1 = a_n + 1
c) s̈_n = (1+i)ⁿ⁺¹ a_n
d) ä_n (1_vⁿ) = ä_2n
e) (s̈_2n / s̈_n) -2 = iS_n
f) S_n = s̈_n-1 +1
All true
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The annual eff. int rate is 4%. An annuity-due makes pmts of $5 at the beginning of each year for 8 years. Find the PVo of the annuity-due.
PVo= 5+5v+5v²+...+5v⁷
- 5ä_8 = 5 (1-v⁻⁸)/d
- = 5* 1-(1/1.04)⁻⁸ / (0.04/1.04)
- = 5(7.0021)
- = 35.01
- OR
- 8[N]4[I/Y]5[PMT][CPT][PV]
- = -33.66
- Then multiply 1+i (1.04)
- = -35.01, then make positive
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The annual eff. int rate is 6%. A perpetuity-due makes pmts of $5 at the beginning of each year forever. Calculate the PVo of the perpetuity-due.
- PVo= 5ä_∞
- = 5(1/d)
- = 5 (1+i / i)
- = 5 (1.06 / 0.06)
- = 88.33
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The annual eff. int rate is 6%. A deferred annuity-immed. makes pmts of $1000 per year for 15 years, after a deferral period of 5 years. Calculate the present value of the deferred annuity-immed.
- PVo= 1000(₅|a_15)
- = 1000vᵏ a_n
- = 1000(1.06)⁻⁵ a_15
- = 1000(1.06)⁻⁵ (1-v¹⁵) / i
- = 1000(1.06)⁻⁵ (1-1.06¹⁵) / 0.06
- = 7,257.56
- OR
- 15[N]6[I/Y]1000[PMT][CPT][PV]
- = PV= -9,712.25
- [FV]0[PV][PMT]5[N][CPT][PV]
- = 7,257.56
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The nominal annual int rate compounded monthly is 9%. A deferred annuity-immed makes pmts of $100 per month for 10 yrs, after a deferral period of 3 years. Calculate the present value of the deferred annuity-immed.
- Eff. monthly int rate is iᵐ/m
- = 0.09/12 = 0.0075
- PVo= 100(₃₆|a_120)
- = 100v³⁶ a_120|0.0075
- = 100(1.0075)⁻³⁶ (1-v¹²⁰) / 0.0075
- = 100(1.0075)⁻³⁶ (1-(1+0.0075)⁻¹²⁰) / 0.0075
- = 100(0.7641)*(78.9417)
- = 6,032.32
- OR
- 120[N]0.75[I/Y]100[PMT][CPT][PV]= -7,894.17
- [FV]0[PMT][PV]36[N][CPT][PV]
- = 6,032.32
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The nominal annual int rate compounded monthly is 9%. A deferred perpetuity-immed make pmts of $100 per month forever, after a deferral period of 3 years. Calculate the PV of the deferred perpetuity-immed.
- Use 1 month as unit of time. Monthly eff, int rate= iᵐ/m = 0.09/12 = 0.0075
- k= deferral period = 36 months
- PVo= 100(₃₆|a_∞|0.0075)
- = 100 v³⁶ (1/0.0075)
- = 100(1.0075)⁻³⁶ (133.3333)
- = 10,188.65
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The nominal int rate is convertible quarterly is 8%. A deferred annuity-due makes pmts of $300 every 3 months for 15 years, after a deferral period of 5 years. Calculate the present value of the deferred annuity-immed.
- PVo= 300(₂₀|ä_60)
- = 300v²⁰ a_60|0.02
- = 300(1.02)⁻²⁰ (1-v⁶⁰ / d)
- = 300(1.02)⁻²⁰ (1-(1.02)⁻⁶⁰ / 0.01960)
- = 300(0.6729)*(35.47029)
- = 7,158.28
- OR
- 60[N]2[I/Y]300[PMT][CPT][PV]= -10,636.83
- [FV]0[PV][PMT]20[N][CPT][PV]= 7,158.28
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