What is a series of equal payments occurring at equal interval of time where the first payment is made after several periods after the beginning of the payment?

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• When the payments are made at the beginning of each payment period the annuity is called?
• When the payments fall due at the beginning of each interval the annuity is called?
• What do you call the time interval to the beginning of the first payment interval?
• When the payments are made at the end of each payment period the annuity is called?

Annuity: A series of equal payments or receipts occurring over a specified number of periods.

Ordinary annuity: A series of equal payments or receipts occurring over a specified number of periods with the payments or receipts occurring at the end of each period.

Annuity due: A series of equal payments or receipts occurring over a specified number of periods with the payments or receipts occurring at the beginning of each period.

WARNING:  While technically correct, the last two definitions shown above can be a bit confusing.  Whether a cash flow appears to occur at the end or the beginning of a period often depends on your perspective. (For example, isn't the end of year 2 also the beginning of year 3?)

Therefore, the real key to distinguishing between an ordinary annuity and an annuity due is the point at which either a future or present value is to be calculated. Remembering the following characteristics should help you to identify the type of annuity that you are dealing with:

1.  For an ordinary annuity, future value is calculated as of the last cash flow, while present value is calculated as of one period before the first cash flow.

2.  For an annuity due, future value is calculated as of one period after the last cash flow, while present value is calculated as of the first cash flow.

The following examples, which make use of a single time line, should help you to identify and value the various annuity patterns:

0        1        2        3        4        5        6  Time line
|--------|--------|--------|--------|--------|--------|
         ¦        R        R        R        R        ¦  Cash flows
         ¦        ¦                          ¦        ¦
        PVA4     PVAD4                       FVA4     FVAD4

NOTE:
PVA4 is valued as of one period before the first cash flow, which is at the end of period 1.
PVAD4 is valued as of the first cash flow, which is at the beginning of period 3.
FVA4 is valued as of the last cash flow, which is at end of period 5.
FVAD4 is valued as of one period after the last cash flow, which is also the beginning of period 7.
 

Present Value of an (Ordinary) Annuity (PVA):

        PVA4 = (R) x (PVIFAi%,4)

Future Value of an (Ordinary) Annuity (FVA):

        FVA4 = (R) x (FVIFAi%,4)

Present Value of an Annuity Due (PVAD):

        PVAD4 = (R) x (PVIFAi%,4) x (1 + i%)
or
        PVAD4 = [(R) x (PVIFAi%,3)] + R = (R) x (PVIFAi%,3 + 1)

Future Value of an Annuity Due (FVAD):

        FVAD4 = (R) x (FVIFAi%,4) x (1 + i%)
or
        FVAD4 = (R) x (FVIFAi%,5) - R = (R) x (FVIFAi%,5 - 1)
 

TIP:  When valuing annuities due, just remember to due the RIGHT thing.  That is, PVADs and FVADs are determined as of one period to the RIGHT of positions assumed for an ordinary annuity with the same cash flows. So, you can treat them initially as ordinary annuities, find the PVA (or FVA), and simply multiply that answer by (1 + i%), which effectively shifts the earlier answer one period to the right.

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When the payments are made at the beginning of each payment period the annuity is called?

2.2 Annuity-Due An annuity-due is an annuity for which the payments are made at the beginning of the payment periods. The time diagram in Figure 2.2 illustrates the payments of an annuity-due of 1 unit in each period for n periods.

When the payments fall due at the beginning of each interval the annuity is called?

Solution. If payments of an annuity fall due at the beginning of every period, the series is called annuity due.

What do you call the time interval to the beginning of the first payment interval?

A payment interval is the time between successive payments. The periodic payment of an annuity is the amount deposited or paid for each payment interval. The term of an annuity is the time from the beginning of the first payment to the end of the last payment interval.

When the payments are made at the end of each payment period the annuity is called?

If the periodic payments are made at the end of each period, the annuity is called an immediate annuity or ordinary annuity.

What is a series of equal payments occurring at equal intervals of time where the first payment is made after several periods after the beginning of the payment?

What is the artificial expense that spreads the purchase price of an asset or another property over a number of years?

What refers to the lessening of the value of an asset due to the decrease in the quantity available?

Which of the following depreciation method Cannot have a salvage value of zero?