
The annual eff. int rate is 4%. An annuityimmed. makes pmts of $5 at the end of each year for 8 years. Find the PV of the annuityimmed.
 PVo= 5v + 5v² + 5v³+...+5v⁸
 = 5(v+v²+...+v⁸)
 = 5a_84%
 = 5(1v⁸/i)
 = 5 ((11.04)⁸) / 0.04
 = 33.66
 OR, use calculator
 8[N]4[I/Y]5[PMT][CPT][PV]
 = 33.66, then make positive

The annual eff. int rate is 4%. An annuityimmed makes level pmts at the end of each year for 8 years. The PVo of the annuityimmed 33.6637. Calculate the amount of each level pmt.
 PVo= (Pmt) a_84%
 33.6637 = (Pmt) ((11.04)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

The annual eff. int rate is 4%. An annuityimmed. makes pmts of $5 at the end of each year for 8 years. Calculate the accumulated value of the annuityimmed. at the end of 8 years.
 AV₈= 5(1.04)⁷+5(1.04)⁶+...+5(1.04)+5
 = 5 * (1.04⁸1) / 0.04
 = 5*(9.2142)
 = 46.07
 OR, use calculator
 8[N]4[I/Y]5[PMT][CPT][FV]
 = 46.07, then make positive

The annual eff. int rate is 6%. A perpetuityimmed. makes pmts of $5 at the end of each year forever. Calculate the PV of the perpetuityimmed.
 PVo= 5a_∞
 = 5(1/0.06)
 = 83.33

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_n1 +1
All true

The annual eff. int rate is 4%. An annuitydue makes pmts of $5 at the beginning of each year for 8 years. Find the PVo of the annuitydue.
PVo= 5+5v+5v²+...+5v⁷
 5ä_8 = 5 (1v⁻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

The annual eff. int rate is 6%. A perpetuitydue makes pmts of $5 at the beginning of each year forever. Calculate the PVo of the perpetuitydue.
 PVo= 5ä_∞
 = 5(1/d)
 = 5 (1+i / i)
 = 5 (1.06 / 0.06)
 = 88.33

The annual eff. int rate is 6%. A deferred annuityimmed. makes pmts of $1000 per year for 15 years, after a deferral period of 5 years. Calculate the present value of the deferred annuityimmed.
 PVo= 1000(₅a_15)
 = 1000vᵏ a_n
 = 1000(1.06)⁻⁵ a_15
 = 1000(1.06)⁻⁵ (1v¹⁵) / i
 = 1000(1.06)⁻⁵ (11.06¹⁵) / 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

The nominal annual int rate compounded monthly is 9%. A deferred annuityimmed makes pmts of $100 per month for 10 yrs, after a deferral period of 3 years. Calculate the present value of the deferred annuityimmed.
 Eff. monthly int rate is iᵐ/m
 = 0.09/12 = 0.0075
 PVo= 100(₃₆a_120)
 = 100v³⁶ a_1200.0075
 = 100(1.0075)⁻³⁶ (1v¹²⁰) / 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

The nominal annual int rate compounded monthly is 9%. A deferred perpetuityimmed make pmts of $100 per month forever, after a deferral period of 3 years. Calculate the PV of the deferred perpetuityimmed.
 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(₃₆a_∞0.0075)
 = 100 v³⁶ (1/0.0075)
 = 100(1.0075)⁻³⁶ (133.3333)
 = 10,188.65

The nominal int rate is convertible quarterly is 8%. A deferred annuitydue makes pmts of $300 every 3 months for 15 years, after a deferral period of 5 years. Calculate the present value of the deferred annuityimmed.
 PVo= 300(₂₀ä_60)
 = 300v²⁰ a_600.02
 = 300(1.02)⁻²⁰ (1v⁶⁰ / 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

