Time Value Of Money Formula's

Front 1

Singleton
Compound Amount
Table: (F|P,i,N)

Back 1

A single present or future cash flow.
F = P(1+i)^N
Year Benefit

Hint 1

P Period zero value
F Period N value
i Interest rate
N Last period

Front 2

Singleton
Present Worth
Table : (P|F,i,N)

Back 2

A single present or future cash flow.
P = F(1+i)^-^N

Hint 2

P Period zero value
F Period N value
i Interest rate
N Last period

Front 3

Constant Series
Compound Amount
Table :(F|A,i,N)

Back 3

A series of flows of equal amounts at regular intervals.
F = A [((1+i)^N-1)/i]

Hint 3

F Period N value
i Interest rate
N Last period
A Used in constant series

Front 4

Constant Series
Sinking Fund
Table: (A|F,i,N)

Back 4

A series of flows of equal amounts at regular intervals.
A = F [i/((1+i)^N-1)]

Hint 4

F Period N value
i Interest rate
N Last period
A Used in constant series

Front 5

Constant Series
Present Worth
Table: (P|A,i,N)

Back 5

A series of flows of equal amounts at regular intervals.
P = A [((1+i)^N-1)/(i(1+i)^N)]

Hint 5

P Period zero value
i Interest rate
N Last period
A Used in constant series

Front 6

Constant Series
Capital Recovery
Table: (A|P, i, N)

Back 6

A series of flows of equal amounts at regular intervals.
A = P[i(1+i)^N/((1+i)^N-1)]

Hint 6

P Period zero value
i Interest rate
N Last period
A Used in constant series

Front 7

Linear Gradient Series
Present Worth
Table: (P|G,i,N)

Back 7

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)]

Hint 7

P Period zero value
i Interest rate
N Last period
G Change in cost or benefit every period in a linear gradient series

Front 8

Linear Gradient Series
Conversion Factor
Table: (A|G,i,N)

Back 8

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])]

Hint 8

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

Front 9

Geometric Gradient Series
Present Worth: (P|A1, g,i,N)

Back 9

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

Hint 9

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

Front 10

Irregular

Back 10

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.

Front 11

Tip:

Back 11

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.

Front 12

Present Value

Back 12

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.

Front 13

Future Value

Back 13

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.

Front 14

Annuity Payment

Back 14

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.

Front 15

Interest Rate

Back 15

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).

Front 16

Number of Periods

Back 16

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

Front 17

Time Value of Money

What does i stand for?

Back 17

it can mean the nominal interest rate, or it could be the effective interest rate

Front 18

Time Value of Money

What does N stand for?

Back 18

N is the number of time the money is going to compound

Front 19

Time Value of Money

What does n stand for?

Back 19

n is a specific instance of N

Front 20

Time Value of Money

What does A stand for?

Back 20

A is used in constant series TMV problems to represent the amount that is being put

Front 21

Time Value of Money

What does A_n (A sub n) stand for?

Back 21

A_n is the cost of benefit is one specific period (n)

Front 22

Time Value of Money

What does G stand for?

Back 22

G is used as the change in cost or benefit in each n for a linear gradient series

Front 23

Time Value of Money

What does g stand for?

Back 23

g is the growth rate and it is used in Geometric Growth Series

Front 24

Time Value of Money

Effective vs Nominal Interest Rate
Which one should you use and why?

Back 24

Most of the time we are given the nominal rate