Interest Theory - (Chapter 7)

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The nominal annual int rate compounded monthly is 12%. Find the present value of an annuity-immediate that makes monthly pmts at a rate of $36 per year for 10 years.
- i¹²/12= 0.12/12 = 0.01 (monthly eff. rate)
- v= 1/1+i = (1+iᵐ/m)⁻ᵐ
- = 1.01
- PVo= 36a¹²_10
- = 36 * (1-v¹⁰ / i¹²)
- = 36 * (1-(1.01⁻¹²)¹⁰) / 0.12
- = 36(5.803)
- = 209.10
The nominal annual int rate compounded monthly is 12%. Find the present value of a perpetuity-immediate that makes monthly pmts at a rate of $36 per year forever.
i¹²/ 12 = 0.12 /12 = 0.01
- PVo= 36a¹²_∞
- = 36 * 1/i¹²
- = 36 * 1/0.12
- = 300
Annuity-immed formula
(Payable monthly)

Annuity-due formula
(Payable monthly)
- PVo= aᵐ_n = 1-vⁿ / iᵐ
- (Where v= (1+i)⁻ᵐ)
- PVo= äᵐ_n = 1-vⁿ / dᵐ
- (Where v= (1+i)⁻ᵐ)
The nominal annual int rate compounded monthly is compounded monthly is 12%. Find the accumulated value at the end of 10 years of an annuity-due that makes monthly pmts. at a rate of $36 per year for 10 years.
i¹²/12= 0.12/12 = 0.01, We need d¹²
- = (1+(iᵐ/m))ᵐ = 1+i = (1-(dᵖ/12))⁻ᵖ
- = 1+(i¹²/12) = (1-(dᵖ/12)⁻¹
- = d¹²/12 = 1-(1+0.01)⁻¹
- = d¹² = 12[1-(1.01)⁻¹]
- = 0.1188
- AV₁₀= 36 s̈¹²_10
- = 36 * (1.01¹²)¹⁰-1 / d¹²
- = 36 * (1.01¹²)¹⁰-1 / 0.1188
- = 697.02
The normal annual int rate compounded monthly is 12%. Find the PV value of a perpetuity-due that makes monthly pmts at a rate of $26 per year forever.
- 1+i = (1+(iᵐ/m)ᵐ = eʳ
- = (1+(iᵐ/12)¹² = eʳ
- r= ln[(1.01)¹²]
- r= 12ln(1.01)
- = 0.1194
- PVo= 36(1-vⁿ / r)
- = 36 * 1-((1.01)⁻¹²⁰)⁻¹⁰ / 0.1194
- = 36 * 1-(1.01)⁻¹²⁰ / 0.1194
- = 36(5.874)
- = 210.15
Perpetuity-immed: PVo=__
Perpetuity-die: PVo=___
Contin. Payable Perpetuity: PVo=___
- Perp.-immed: PVo= 1/i
- Perp.-due: PVo= 1/d
- Contin. Payable Perp: PVo= 1/r

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Interest Theory - (Chapter 7)

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2024-10-01T01:08:27Z

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