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Calculate the equivalent nom. annual discount rate compounded quarterly

dᵐ/m = (iᵐ/m) / (1+(iᵐ/m))
If we have two equivalent discount rates, use the following formula:

(1-(dᵐ/m))ᵐ = PVo = (1-(dᵖ/p))ᵖ
Force of int formula

AVt = PVo *eʳᵗ
If all you're given is r (force of interest):

1) Annual eff. int rate
2) Nom. annual int. rate convertible quarterly
3) Nom. annual discount rate convertible monthly
4) Annual eff. discount rate
- 1)eʳ = 1+i
- (Solve for i)
- 2) eʳ = (1+(iᵐ/m))ᵐ
- (Solve for i⁴)
- 3) eʳ = (1-(dᵖ/p))⁻ᵖ
- (Solve for d¹²)
- 4) eʳ = (1-d)⁻¹
- (Solve for d)
... "compounded semiannually"

AVt = PVo(1+(iᵐ/2)²ᵗ
... "convertible monthly"

AVt = PVo(1+(iᵐ/12))¹²ᵗ
Nom. annual int. rate is ... Calculate the equiv. force of int. if we assume a compounding frequency of:

1) Once a yr
2) Quarterly
3) 24 times per yr
- The base formula is really:
- eʳ= (1+i) [For 1 yr] OR eʳ= (1+(iᵐ/m))ᵐ [Multiple yrs]
1) r= ln(1+i)

2) r= 4ln(1+(iᵐ/m))

3) r= 24ln(1+(iᵐ/m))
1)What is the annual compound discount rate?

2) What is the discount factor v?

1) d= i / (1+i)

2) v= 1 / (1+i)

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Updated

2024-09-16T16:49:29Z