In this series we’ve learned about the time value of moneyfuture value; present value; calculating payment; and calculating interest rate. This week we will learn about number of periods remaining. Calculating number of periods will show us how many monthly payments we have left on a loan.

Calculating Number of Periods:

Time-Value-of-Money-Timeline Calculating Number of Periods: How Many Payments do you have Left?
To refresh your memory, N is the number of periods. For example, N on a 30-year mortgage is 360. 30 years multiplied by 12 months in a year.  We will solve for the number of periods remaining on your home mortgage in this example.  If you need a full refresher, review my time value of money post.

How much longer do I have to pay my mortgage?

You purchased your dream home 7 years ago. And you love your house but man are you tired of paying the mortgage. Does it ever end? At this rate, you’ll have to work forever. You’re almost desperate enough to click on one of those spam mortgage forgiveness ads on the internet.

Let’s look at what we do know:

Ok. I get it. The answer is 23 and you didn’t even need a calculator. Aren’t you smart?
Ignore the easy answer for now. This is just an easy example almost everyone can relate to. Let’s work on calculating number of periods so you can use these math skills later in life.

Find I/Y (Interest per Year)

The bank tells you this one. In this example, let’s use 3.45%. This is a low interest rate but it’s the quoted rate on Bankrate.com as of 9/13/16.  Divide 3.45% by 12 because you will make monthly payments.

Find PMT (Payment)

You took out a 30-year mortgage with a 3.45% interest rate. And used a $100,000 loan to buy your home. With these assumptions, let’s calculate PMT (Payment). Here’s the summary of inputs for a financial calculator:
N: 360
I/Y: 0.2875% (3.45%/12 because this is I/Y per N.  3.45% for I/Y would equate to 41.4% per year)
PV: $100,000
FV: $0
Your monthly principle and interest payment is $446.26.

Find PV (Present Value)

This one is a little trickier. We need to find the PV (Present Value) 7 years into the loan. This will take some calculations. We will actually solve for FV (Future Value) in this mini-problem. Here’s the summary of inputs for a financial calculator:
N: 84 (7 multiplied by 12)
I/Y: 0.2875% (3.45%/12 because this is I/Y per N.  3.45% for I/Y would equate to 41.4% per year)
PV: $100,000
PMT: -$446.26 (PMT (Payment) from above)

On your calculator, hit CPT then FV.  The future value is $84,940.36.  This means we have a loan balance of $84,940.36 after 7 years of payments.

Here’s the formula to solve the problem in a spreadsheet program such as Apache OpenOffice:
=FV(.0345/12, 7*12, 100000, -446.26)

Find FV (Future Value)

This one is the easiest in this example. The FV (Future Value) is $0 because you will have a zero balance at the end of the loan.

Solve for the number of payments you have left by calculating number of periods:

Here’s the summary of inputs for a financial calculator:

I/Y: 0.2875% (3.45%/12 because this is I/Y per N.  3.45% for I/Y would equate to 41.4% per year)
PV: $84,940.36
PMT: -$446.26
FV: $0

On your calculator, hit CPT then N.  The number of periods left is 276 and means you have 276 loan payments left.

Here’s the formula to solve the problem in a spreadsheet program such as Apache OpenOffice:
=NPER(0.0345/12,-446.26,84940.36,0)

Are you having trouble calculating number?  Ask your questions in the comments below.

This wraps up my time value of money series for now. In the future, I will dig back in with more complex problems.

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