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24 Cards in this Set

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Singleton
Compound Amount
Table: (F|P,i,N)
A single present or future cash flow.
F = P(1+i)^N
Year Benefit
P Period zero value
F Period N value
i Interest rate
N Last period
Singleton
Present Worth
Table : (P|F,i,N)
A single present or future cash flow.
P = F(1+i)^-^N
P Period zero value
F Period N value
i Interest rate
N Last period
Constant Series
Compound Amount
Table :(F|A,i,N)
A series of flows of equal amounts at regular intervals.
F = A [((1+i)^N-1)/i]
F Period N value
i Interest rate
N Last period
A Used in constant series
Constant Series
Sinking Fund
Table: (A|F,i,N)
A series of flows of equal amounts at regular intervals.
A = F [i/((1+i)^N-1)]
F Period N value
i Interest rate
N Last period
A Used in constant series
Constant Series
Present Worth
Table: (P|A,i,N)
A series of flows of equal amounts at regular intervals.
P = A [((1+i)^N-1)/(i(1+i)^N)]
P Period zero value
i Interest rate
N Last period
A Used in constant series
Constant Series
Capital Recovery
Table: (A|P, i, N)
A series of flows of equal amounts at regular intervals.
A = P[i(1+i)^N/((1+i)^N-1)]
P Period zero value
i Interest rate
N Last period
A Used in constant series
Linear Gradient Series
Present Worth
Table: (P|G,i,N)
A series of flows the increases or decreases by a set amount and regular time intervals.
P = G [((1+i)^N-iN-1)/(i^2(1+i)^N)]
P Period zero value
i Interest rate
N Last period
G Change in cost or benefit every period in a linear gradient series
Linear Gradient Series
Conversion Factor
Table: (A|G,i,N)
A series of flows the increases or decreases by a set amount and regular time intervals.
A = G[((1+i)^N-iN-1)/(i[(1+i)^N-1])]
P Period zero value
F Period N value
i Interest rate
N Last period
n Some time
A_n Cost or benefit in period n
A Used in constant series
G Change in cost or benefit every period in a linear gradient series
g Growth rate in a geometric gradient series
Geometric Gradient Series
Present Worth: (P|A1, g,i,N)
A series of flows that increases or decreases by a fixed percentage at regular intervals.
P = A1[(1-(1+g)^N(1+i)^-N)/(i-g)] or P = A1(N/(1+i)) if i=g
P Period zero value
i Interest rate
N Last period
A_n Cost or benefit in period n
g Growth rate in a geometric gradient series
Irregular
A series of flows that does not exhibit an overall pattern. Patterns can sometimes be detected within the irregular pattern allowing it to be subdivided into one of the more familiar patterns.
Tip:
Every time value of money problem has five variables: Present value (PV), future value (FV), number of periods (N), interest rate (i), and a payment amount (PMT). In many cases, one of these variables will be equal to zero, so the problem will effectively have only four variables. You will always know the values of all but one of these, and it is that missing value for which you will be solving.
Present Value
Any value that occurs at the beginning of the problem (or the beginning of a part of the problem) is a present value. The key is that the present value occurs before any other cash flows. Usually, when a present value is given, it will be surrounded by words indicating that an investment happens today.
Future Value
The future value is usually the last cash flow. Obviously, it is a cash flow that occurs at some time period in the future. The future value is a single cash flow. If it occurs more than once, then it is probably an annuity payment.
Annuity Payment
An annuity payment is a series of two or more equal payments that occur at regular time periods. Each payment, if taken alone, is a future value, but the key point is that the annuity payment is a recurring payment. That is, there are more than one of them in a row.
Interest Rate
The interest rate is the growth rate of your money over the life of the investment. It is usually the only percentage value that is given. However, some problems will have different interest rates for different time frames. For example, problems involving retirement planning will often give pre-retirement and post-retirement interest rates. Frequently, when you are being asked to solve for the interest rate, you will be asked to find the compound average annual growth rate (CAGR).
Number of Periods
The number of periods is the total length of time that the investment will be held. Typically, it is given as a number of years, though it will often need to be adjusted to some other time scale. For example, if you are told that the investment pays interest quarterly (4 times per year) then you must adjust N so that it reflects the total number of quarterly (not annual) time periods
Time Value of Money

What does i stand for?
it can mean the nominal interest rate, or it could be the effective interest rate
Time Value of Money

What does N stand for?
N is the number of time the money is going to compound
Time Value of Money

What does n stand for?
n is a specific instance of N
Time Value of Money

What does A stand for?
A is used in constant series TMV problems to represent the amount that is being put
Time Value of Money

What does A_n (A sub n) stand for?
A_n is the cost of benefit is one specific period (n)
Time Value of Money

What does G stand for?
G is used as the change in cost or benefit in each n for a linear gradient series
Time Value of Money

What does g stand for?
g is the growth rate and it is used in Geometric Growth Series
Time Value of Money

Effective vs Nominal Interest Rate
Which one should you use and why?
Most of the time we are given the nominal rate