**Payment Factor = r ÷ [1 – (1 + r) ^{-n} ]**

P = payment

r = rate

n = number of periods

Annuity payment factor is used to calculate annuity for a payment and to simplify the calculations steps. The formula above particularly focuses on the annuity payment calculations where the present value of annuity is known as opposed to the known future value of annuity.

Similarly, one must have to take care about the rate and period involved in the calculations. Any calculation involving rate and period requires the matching or fusion of both rate and period at the same scale. For instance, if payments are made or received on monthly basis, then the rate must also be on monthly basis.

## How annuity payment factor is useful for investors

The prime focus and usefulness of the above equation is to simplify the procedure and to allow quick calculations without annuity table. Annuity payment factor formula tries to figure out annuity where present value is known. Another way to do this which is a traditional method is by using annuity table to find respective annuity factor. After that, we multiply both annuity factor and original payment to determine the annuity for that specific period.

Annuity payment factor is useful for investors and financials analysts in multiple terms while either for budgeting, investments analysis and multiple other needs. For example, annuity factor can be used to calculate the profitability of an investment project when used in relation with multiple other ratios. However, one can also use it to figure out the profitability of shares when used along with other ratios including capital yield or dividend yield ratios.

### Annuity payment factor formula example

Mr. Jason runs a company of garments which sells jeans pants. Currently he is looking in to calculate monthly payments project where he will get an original balance of $5,000 which will be paid in 36 months on the basis of 12% annual rate but compounded monthly. For that, we have to first find the annuity factor by using formula above or by using annuity table. The annuity factor for 3 years at monthly rate of 1% will be 0.01431 and we can get monthly payments by multiplying both values.

Monthly payments = $5,000 × 0.01431

= $71.54

### How annuity payment factor is established

Basically, annuity payment factor formula which uses present value is derived by taking out present value portion from __annuity payment formula__. The annuity payment formula is presented as;

P = [r × (PV)]÷ [1 – (1 + r)^{-n} ]

We can rewrite or rearrange the above equation as;

P = PV × { r ÷ [1 – (1 + r)^{-n} ]}

Now if we take out the PV from the above equation then the formula becomes more simplify to calculate the annuity payment factor. We can then use this factor to create an annuity table for a number of terms and rates.