## What Are Periodic Payments?

There are two ways that you can look at periodic payments and we will take a look at both within this article so that you can understand what each is and how they are calculated. Also, our online finance tutor website will explore you the secrets of periodic payments calculation.

**Annuity periodic payments**

The first definition of a periodic payment is the payment that is disbursed from a financial plan or annuity such as that purchased by a private pension or retirement plan. These payments are made on a regular basis which could be anything from monthly to annually to provide a regular income to the holder of the plan.

These types of payments can be based purely on the return that the principle investment generates or it may return a portion of the principle over a fixed number of years along with the return. There are several different types of plans that can be purchased and with different tax rules. Some may allow the payment of taxes to be deferred while others may have taxes paid up front and then offer periodic payments that are tax free.

**Amortization periodic payment**

The second type of periodic payment that we will consider is that of the periodic payments that are required to pay off a loan. This is typically for a mortgage or car loan. Calculations are performed to find the fixed amount required to pay every month that will end with a zero balance at the end of the full term.

During the term the amount of the periodic payment that goes towards interest and the principal amount of the loan will vary. At the start of the loan the majority of the payment is for interest and for the principal amount at the end of the period.

## Periodic Payment Formula for Calculating Annuity Payments

The annuity payment formula is what you will use to calculate periodic payments over the period of the plan. The following is the formula that you will apply:

**P= r (PV) / ( 1 – (1 + r) -n**P = Payment to be received

PV = Present Value

R = Rate per period

N = Number of periods

This formula assumes that the rate is not going to change and that the payment will be constant, also that the first payment will be one period away. If the payment or the rate changes then the calculation would need to be redone.

If however the payments are to grow at a proportionate rate then a different formula needs to be used to calculate PMT (periodic payment). The following formula is used when payments will grow at a fixed rate:

**Initial Payment = PV x (r – g) / [ 1 – ( (1 + g) / (1 + r))n ]**PV = The Present Value

R = rate per period

G = growth rate

N = number of periods

There are several other alternative formulas that you can use for calculating the periodic payment of annuity depending on a host of other variables. You should always select the one that you need with great care. Choosing the wrong one could result in a very wrong answer.

Always be clear before you start your assignment as to exactly what is being asked of you and double check that you are selecting the right formula for your case before you begin you calculations. Checking your financial formulas calculation with one of the many online calculators is advised so that you can see if your working out has been done correctly.

## Amortization Periodic Payment Formula

To figure out the periodic payments that you need to make to pay off a loan or a mortgage requires a very different formula to that being used above. The following formula is the one that you will need to implement to calculate the periodic payments required to clear the loan within the specified period:

**P = L [ c(1 + c)n ] / [ (1+c)n – 1 ]**P = periodic payment required

L = The loan amount ($)

c = The monthly interest rate ( If the quoted rate is 6% then it is 0.06/12 = 0.005)

n = The number of months the loan is over ( So if 10 years = 120 months)

Another calculation that you may be asked for is to discover the outstanding balance after the loan has been paid for a number of months. This can be calculated with the following formula:

**B = L [ c(1 + c)n – (1 + c)p ] / [ (1+c)n – 1 ]**B = Outstanding balance

L = The loan amount ($)

c = The monthly interest rate

p = The number of months payment has been made for

n = The number of months the loan is over

## Problems with Doing Periodic Payment Homework Assignments

No matter how you look at it, finance can be one of those areas in which even gifted students can struggle. Some of the ideas and concepts are hard to understand and the formulas that you need to understand and use can be difficult to say the least. Many students struggle to implement formulae correctly especially when they have many terms in brackets that will need to be done in the correct order. This tends to result in students reaching the incorrect answer even if they have used the correct formula.

The following tips for doing your homework in finance will help you to get any questions about periodic payments correct:

- Pay attention within the class and do the related reading that you have been set. Typically your homework will build on what has been covered rather than expecting you to go off and discover something completely new on your own.
- Be clear as to what you are being asked to do for your assignment, such as understanding the actual type of periodic payment you are being asked to calculate. If it is not completely clear to you ask your tutor for clarification.
- Use the internet to find the formula that you need; but do not just accept everything as being accurate. There are many websites that may list completely the wrong formula for what you actually need. Check and double check rather than using without thought.
- Work with a study team so that you get a better understanding of how to solve the problems that you have been set. Do not however simply copy the same answer from each other.
- Compare your results with an online periodic payment calculator, although do ensure that you will be calculating the same thing as there are many options.
- Always double check and proofread your answers to avoid any errors before you submit your assignments.

## Using a Periodic Payment Calculator

There are many websites that will take out the difficulties of doing the calculations for you by providing you with an online equation solver that will provide you the answers that you need quickly and accurately. As with looking for your formulas online however you do need to ensure that you select the right calculator to perform the actual calculation that you need. Online calculators are an ideal way to see if your own personal calculation has been performed correctly and should always be used to double check your own work. They work very simply and most have very clear prompts for collecting the data required for the calculations to make it easy for you.

These tools are often more aimed at personal or business use rather than for use with your assignments, as such they may not actually show the calculation formulas that are used. When you do your assignment it is always best to show your working so that your tutors knows that you understand the calculations being undertaken. The following are some of the calculators that you could use for doing periodic payment calculations:

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