I get many calls asking for help understanding how to use a financial calculator, especially figuring yields on mobile home deals. I hope this clears up some of the confusion you may have and to help you structure better, more profitable deals.
The power of the financial calculator has changed the world of investing. Numerical problems that were once very difficult, almost impossible for the average investor to figure out, are now solved in seconds with a little $30 calculator.
Yet many investors, or would be investors, still look on this little pocket-sized machine as too intimidating or too difficult to learn to use. Not so. If you’re serious about becoming a successful investor, I can’t imagine trying to do business without one.
Let’s start by learning what all those strange looking keys mean. And be sure you have a financial calculator, not some little calculator that’s designed to do simple math problems. Also, be sure that you have it programmed for the financial mode.
Your instruction manual will show you how, so spend some time studying the manual before you start trying to do examples. If it’s not programmed correctly, you won’t get correct answers.
There are some good, inexpensive financial calculators on the market. The Hewlett Packard HP 10B and the Texas Instrument BA 35, are both excellent machines. They cost about $30 and will do everything you will need to do.
All financial calculators are basically the same. Some are just more advanced and more sophisticated than others. But they all have the primary five keys that you will be using to solve most mathematical problems. These five keys are normally in the first or second row of your calculator:
* N = Number of Payments
* I = Interest, or Yield/Return
* PMT = Payment
* PV = Present Value, or Loan Amount
* FV = Future Value
The following table shows how these keys will be displayed in the examples in this article. The top row of our table represents the key functions required to solve the calculations. The next row will be the figures used in our calculation examples.
These are the actual figures you will enter into the proper boxes. If you will get familiar with this type table or format, it will be much easier to plug the appropriate numbers into the appropriate boxes to solve your calculations. So start thinking N, I, PMT, PV & FV.
Our standard table
|
N |
I |
PMT |
PV |
FV |
In most cases, we will only be using four key strokes: N, I, PMT & PV. Anytime you know any three of these four functions, you can easily solve for the fourth. In the following example our unknown function is N (number).
But before we get into punching the buttons and doing examples, check and see if you have your calculator programmed correctly. Try the following example to see if you get the correct answer. And if you haven’t already done so, set your display to show two decimal places.
Let’s say you plan on making a $10,000 loan, amortized over 10 years (120 monthly payments), at 10% annual interest rate. Since the loan is based on monthly payments, the 10% annual interest rate must be reduced to a monthly rate.
Some calculators will do this automatically. If yours doesn’t, then you need to divide the 10% annual interest rate by 12 to get a monthly rate, which will be 0.83. Check your manual.
Also, some calculators require that either the payment amount (PMT), or the loan amount (PV) be a negative number. The default setting for both the payment number, and the loan number will be positive numbers when entered. So you will need to change one to a negative number. Otherwise, you will get “error” when you try to solve for the answer.
The best way to ensure that the numbers are entered correctly is to think of the outgoing number (cash out) as a negative number. And the incoming number (cash in) as the positive number.
One more thing before we start doing some examples. Always clear your calculator memory before starting a new function. Some calculators have “constant memory.” This means that any numbers from the previous calculation will remain in the registers unless you clear them.
So get in the habit of clearing all registers before starting a new function. If you don’t already know how to do this, check your instruction manual that came with your calculator and learn how, before proceeding.
Now, let’s see if your calculator is correctly programmed and gives the correct answer to our example. Plug $10,000 into PV, 120 into N, 10% (0.83 monthly rate) into I, and solve for the payment amount. You should get $132.15 for the monthly payment.
If you got anything else, your calculator isn’t programmed correctly, or you punched the wrong buttons. So go back and study your manual to see what you did wrong.
Charlie’s $5,000 loan
Assuming you got the correct answer to that example, let’s do another. Suppose we loan our friend Charlie $5,000, and he promises to pay us $150 each month, including 12% interest until the loan is paid off. In this example, we already know three of the four functions (I, PMT, PV) necessary to complete this transaction.
We know the amount (PV) of the loan ($5,000), we know the interest rate (I/Y) is 12%, and we know the amount of the payment (PMT) is $150. But we don’t know the number of payments that it will take for Charlie to pay us back our $5,000. So what do we need to do in order to solve the puzzle and learn how many payments Charlie will make us?
Let’s create a table so you can better understand how this is done. The FV (future value) key isn’t needed in this calculation, so it’s not included in our table.)
Solving for the unknown function
| N | I | PMT | PV |
| ??? | 1 | 150 | 5,000 |
These are the key strokes you would make to complete this calculation to determine how many payments Charlie would make us. Incidentally, there is no particular order required to enter these figures. Simply enter the three known functions (figures) in any order, and your calculator will solve for the unknown function.
Since we are loaning Charlie $5,000 today, this would be considered the present value (PV), and that figure would go in the PV box. The interest rate is 12%, but that’s an annual rate. Since we’re figuring this loan on a monthly payment basis, we have to break it down to a monthly interest rate.
So we simply divide 12 (number of months) into our 12% interest rate (some calculators will do this automatically) and we have a monthly rate of 1%. This goes into the I box. Charlie has already said he can afford payments of $150 each month on this loan, so that number goes in the PMT (payment) box.
So we now have the loan amount ($5,000) in the PV box, the interest rate (1%) in the I box, and the payment amount ($150) in the PMT box. But we have a question mark in the N box. And that’s because we don’t know the number of payments it will take to amortize this loan based on our three known figures.
So what do we need to do to get the correct figure in the N box? Just punch the N key, and presto… up pops 41. Our calculator is telling us that it will take 41 payments of $150 each, at 12% interest, for Charlie to pay off our $5,000 loan.
Number of payments to pay off the loan
| N | I | PMT | PV |
| 41 | 1 | 150 | 5,000 |
But our calculator has fibbed
Now, I need to point out something in this example that’s not entirely accurate. Even though our calculator tells us that it will take 41 payments to pay this loan off, that’s really not the exact figure.
What happened in this case is our calculator has rounded the number of payments off and says it will take 41 payments. But when we check our calculations another way, we find that our calculator has told us a little fib. It has given us a figure that’s very close, and one which we can now use to fine tune the exact payment amount.
Let’s make another chart so you will understand what happened.
Checking our next table, we see that when we plug 41 in the N box, $5,000 into the PV box, 1% into the I box, and punch the PMT key, instead of the payment being $150, it will be $149.26. So if we had left it like it was and collected 41 payments of $150 from Charlie, we would be collecting more than we were entitled to receive.
Correct Payment Amount
| N | I | PMT | PV |
| 41 | 1 | 149.26 | 5,000 |
So remember, anytime the unknown function is N (number of payments), you will usually get an incorrect payment amount because our calculator rounds off the number of payments (41 in this example). So if we now consider that PMT is the unknown function, and re-enter the other known functions, we get $149.26 as the correct payment, instead of $150.
But, suppose we chose to just leave the number of payments at 41, and the payment amount $150. Could we work with these figures? No, not unless we adjust either the loan amount, or the interest rate. To illustrate, let’s first adjust the interest rate so that it will conform to a $5,000 loan with 41 monthly payments of $150. Check our next chart.
Clear your calculator and plug 41 in the N box, 150 in the PMT box, 5,000 in the PV box, and hit the I button. You should get 1.03 for the interest rate. But since that’s a monthly interest rate, you will need to multiply that figure by 12 to get the annual rate. And when you do, we see that the annual interest rate changes from 12%, to 12.31%.
This shows us that if we make a $5,000 loan, and receive 41 payments of $150, the annual interest rate is 12.31%, not 12%.
Solving for Correct Interest Rate
| N | I | PMT | PV |
| 41 | ??? | 150 | 5,000 |
Correct Interest Rate
| N | I | PMT | PV |
| 41 | 1.03 | 150 | 5,000 |
Now, let’s make one more chart to show what happens if we leave the number of payments at 41, the interest rate at 12%, and the payment amount at $150. This illustration shows that by using these figures, the loan amount will change to $5,024.95.
Solving for Correct Loan Amount
| N | I | PMT | PV |
| 41 | 1 | 150 | 5,024.95 |
I’ve had this sort of thing happen many times when I was structuring a note on a mobile home sale. By using the figures my buyer quotes (down payment and monthly payment amounts), I can structure an amortization schedule that will be workable and affordable for my buyer.
And, in most cases, I can usually make the note a little better by decreasing the number of payments, and increasing the amount of the payment. And I can still keep the payment affordable. For instance, suppose instead of making Charlie a $5,000 loan, we sold him a mobile home and took back a $5,000 note. We see that if I received 41 payments, I would be getting $149.26 instead of $150.
But rather than drop the payment amount to $149.26, I would re-enter the numbers using 40 as the number of payments, instead of 41, and then solve for the PMT. And by doing that, our chart shows us the payment would be $152.28, instead of $149.26.
Solving for 40 Payments
| N | I | PMT | PV |
| 40 | 1 | 152.28 | 5,000 |
Then I would say to Charlie, “If we make it an even 40 months, the payment would be $152.28. Would that work for you?” And in all probability the buyer will agree to the higher payment, which increases my yield, but without a significant change in the monthly payment.
So if you need to change the figures, try to increase, rather than decrease, the payment amount, as long as it’s still affordable for your buyer.
Solving for a balloon payment
You see an ad in you local paper for a house for sale by the owner. The price is $100,000, with 10% down, 9% owner financing for 20 years, and a balloon payment due in 5 years.
The amount of the monthly payment isn’t listed, so you whip out your calculator to see what the monthly payments would be. Our table shows how we enter the numbers. In this example we have to solve for both the payment amount and the balloon amount.
Solving for Monthly Payment Amount
| N | I | PMT | PV |
| 240 | .75 | ??? | 90,000 |
Remember, we have to reduce the yearly interest rate, to a monthly rate. Also, the note will be amortized over a 20 year period, but our payments are figured monthly, so 240 goes in the N box. Enter all the numbers in the appropriate boxes, punch the PMT key, and see if you get $809.75. Piece of cake, huh?
Solving for Monthly Payment
| N | I | PMT | PV |
| 240 | .75 | 809.75 | 90,000 |
Figuring balloon payments
Now we need to figure the amount of the balloon payment that will be due after 5 years. If we make 60 payments, that would leave 180 payments due. To figure the balloon amount, plug in the number of payments remaining, (180) in the N box.
The payment amount ($809.75) stays in the PMT box, and the monthly interest rate (.75) stays in the I box. Our unknown function now is PV, the amount of the balloon payment. So punch the PV button and we see that the payoff balance will be $79,836.01. This is the amount of the balloon payment after 60 payments have been made.
Solving for Balloon Payment Amount
| N | I | PMT | PV |
| 180 | .75 | 809.75 | ??? |
Balloon Payment (PV) Amount Due
| N | I | PMT | PV |
| 180 | .75 | 809.75 | 79,836.01 |
Figuring the balance on your mortgage
Have you ever wondered what the balance was on your mortgage at some point, but just had to take the word of your mortgage company? If so, you will now be able to make several key strokes on your calculator and have your answer instantly. Let’s do an example.
Suppose that several years ago you found your dream house. The sales price was $100,000. After shopping around for a loan, you found a friendly banker willing to loan you 85% of the purchase price. You put up $15,000 for the down payment, and your bank loaned you $85,000 at 9% fixed rate, for 30 years (360 payments). Let’s make a table and see what your payments will be.
Solving for Monthly Payments
| N | I | PMT | PV |
| 360 | .75 | 683.93 | 85,000 |
We see that your payments will be $683.93 per month, P & I (principal & interest). This payment represents both the principal and interest on your loan, which will amortize (pay your loan off) in 30 years (360 payments).
Now, suppose after making 51 payments, you want to know what your loan balance is. Your loan was structured for 360 payments and you’ve made 51, so that leaves 309 payments to go. So enter 309 in the N box, .75% (8% APR) in the I box, $683.93 into the PMT box, and solve for the PV (loan balance).
And we see that your loan balance, after making 51 payments, is $82,128.57.
Solving for koan balance
| N | I | PMT | PV |
| 360 | .75 | 683.93 | 82,128.57 |
Figuring yield
“How do I figure my yield?” is a question I get all the time. So let’s do an example to illustrate how this is done. You buy a mobile home for $3,000, sell it for $6,000, with $600 down and a note for $5,400, 12.75% interest, with 32 payments of $199.95. This is what your buyer will pay you if the note runs the entire term.
How Note is Structured
| N | I | PMT | PV |
| 32 | 1.06 | 199.95 | 5,400 |
To figure your yield, enter the amount that you have LEFT in this deal ($2,400) in the PV box. (You don’t need to reenter the other numbers again, they are still there from the previous calculation, unless you cleared the memory.) Now, punch the I button and you get 90.12%. That’s your yield on this little mobile home deal.
Figuring Your Yield
| N | I | PMT | PV |
| 32 | 1.06 | 199.95 | 5,400 |
Okay, now that you know how to punch the buttons, go do some deals. You are now armed and dangerous with a powerful machine. Happy investing!