CL’s Handy Formula Sheet - Arkansas Tech University
CL's Handy Formula Sheet
(Useful formulas from Marcel Finan's FM/2 Book) Compiled by Charles Lee 8/19/2010
a(t)
Period when greater
Interest Simple Compound
Interest Formulas
Force of Interest
Interest
Discount
Simple
Compound
The Method of Equated Time
The Rule of 72 The time it takes an investment of 1 to double is given by
Date Conventions Recall knuckle memory device. (February has 28/29 days)
Exact o "actual/actual" o Uses exact days o 365 days in a nonleap year o 366 days in a leap year (divisible by 4)
Ordinary o "30/360" o All months have 30 days o Every year has 360 days o
Banker's Rule o "actual/360" o Uses exact days o Every year has 360 days
Basic Formulas
Basic Equations Immediate
Annuities
Due
Perpetuity
Perpetuity
Annuities Payable More Frequently than Interest is Convertible Let = the number of payments per interest conversion period Let = total number of conversion periods Hence the total number of annuity payments is
Coefficient of is the total amount paid during on interest conversion period
Immediate
Due
Annuities Payable Less Frequently than Interest is Convertible Let = number of interest conversion periods in one payment period Let = total number of conversion periods
Hence the total number of annuity payments is
Immediate
Due
Perpetuity
Continuous Annuities
Varying Annuities
Arithmetic
Immediate
Due
General
P, P+Q,...,
P+(n-1)Q
Increasing P = Q = 1
Decreasing P = n Q = -1
Perpetuity
a = 1 r = 1+k
k i If k = i a = 1 r = 1-k k i
If k=i
Geometric Perpetuity
Continuously Varying Annuities Consider an annuity for n interest conversion periods in which payments are being made continuously at the rate and the interest rate is variable with force of interest .
Under compound interest, i.e.
, the above becomes
Rate of Return of an Investment
Rate of Return of an Investment Yield rate, or IRR, is the interest rate at which Hence yield rates are solutions to NPV(i)=0
Discounted Cash Flow Technique
Interest Reinvested at a Different Rate Invest 1 for n periods at rate i, with interest reinvested at rate j
Invest 1 at the end of each period for n periods at rate i, with interest reinvested at rate j
Invest 1 at the beginning of each period for n periods at rate i, with interest reinvested at rate j
Uniqueness of IRR Theorem 1
Theorem 2 Let Bt be the outstanding balance at time t, i.e. o o Then o o
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