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CHAPTER 2: Factors: How Time and Interest Affect Money - Coggle Diagram
CHAPTER 2: Factors: How Time and Interest
Affect Money
UNIFORM SERIES INVOLVING P/A AND A/P
(2) Cash flow amount is same in each interest period
Standard Factor Notation
P = A(P/A,i,n)
A = P(A/P,i,n)
P is one period Ahead of first A value
(1) Cash flow occurs in consecutive interest periods : :
UNKNOWN RECOVERY PERIOD, n
Unknown recovery period problems involve solving for n, given
i and 2 other values (P, F, or A)
Procedure:
Set up equation with all symbols involved and solve for n
FACTOR VALUES FOR UNTABULATED i or n
3 ways
Use spreadsheet function with corresponding P, F, or A value set to 1
Linearly interpolate in interest tables
Use formula
ARITHMETIC GRADIENTS
G starts between periods 1 and 2 (not between 0 and 1). This is because cash flow in year 1 is usually not equal to G and is handled separately as a base amount
Note that P(G) is located Two Periods Ahead of the first change that is equal to G
Arithmetic gradients change by the same amount e ach period
Arithmetic gradient can be converted into equivalent A value using G(A/G,i,n)
UNIFORM SERIES INVOLVING F/A AND A/F
(2) Last cash flow occurs in same period as F
F takes place in the same period as last A
(1) Cash flow occurs in consecutive interest periods
SINGLE PAYMENT FACTORS (F/P AND P/F)
DOWN: P = F[1 / (1 + i )^n]
Factors are represented in standard factor notation such as (F/P,i, n), where letter to left of slash is what is sought; letter to right represents what is given
UP: F = P(1 + i )^n
UNKNOWN INTEREST RATE, i
Unknown interest rate problems involve solving for i, given n and 2 other values (P, F, or A)
Procedure:
Set up equation with all symbols involved and solve for i
GEOMETRIC GRADIENTS
Use following equation for g ≠ i:
Pg = A {1 --[(1+g)/(1+ n }/(i g)
where: A = cash flow in period 1
g = rate of increase
If g = i, Pg = A 1 n/(1+i)
Geometric gradients change by the same percentage each period
If g is negative, change signs in front of both g values