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Amortization of $1:
Amortization of $1 is the process of paying off a $1 loan over a set period of time through regular payments. Just like with a larger loan, these payments would cover both the interest and the principal, or the original amount borrowed.
PMT = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
PMT is the monthly payment
P is the principal amount (the total amount of the loan)
r is the monthly interest rate (annual interest rate divided by 12)
n is the number of payments (total months)
To get the amortization of $1, you would set P to 1 and calculate the result. This will give you the monthly payment per $1 of loan.
Once you have the amortization of $1, you can multiply it by any loan amount to find the monthly payment for that loan. For example, if you're considering a $200,000 loan, you would multiply the amortization of $1 by 200,000.
Keep in mind that the above formula assumes a fixed interest rate and regular, equal payments throughout the life of the loan, which is the standard setup for a mortgage. Other types of loans may require different calculations.
Imagine you borrow $1 from a friend, and you agree to pay it off over 12 months. Each month, you make a payment that covers the interest you owe on the loan (if any) and a portion of the principal. Over time, your loan balance decreases until it's fully paid off. This process is called amortization, even though the amount is quite small. See "Mortgage Constant". One of the six functions of a dollar found on standard financial tables.
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A few more important points about the "Amortization of $1":
Loan Calculators: Today, most people use online loan calculators to figure out their potential monthly payments. These calculators essentially do the same math described above but can handle more complex scenarios and adjustments.
Principal vs. Interest: Keep in mind that the "amortization of $1" gives you the total monthly payment, which includes both the principal (the money you borrowed) and the interest (the cost of borrowing that money). Over time, the proportion of each payment that goes toward the principal versus the interest will change, even though the total payment stays the same.
Changing Interest Rates: The "amortization of $1" figure is based on a fixed interest rate. If you have a variable-rate loan, where the interest rate can change over time, the "amortization of $1" value would not accurately predict your payments.
Different Loan Terms: The "amortization of $1" value will change based on the length of your loan. Longer loans will have a smaller "amortization of $1" (meaning lower monthly payments) because you're spreading out the payments over a longer time. But remember, a longer loan term also means you'll end up paying more in total interest over the life of the loan.
The HP12C financial calculator is a common tool used by real estate and finance professionals to perform these kinds of calculations. Here's how you could use it to determine a monthly mortgage payment, using the "amortization of $1" method:
Let's use the example of a $200,000 loan at a 4% annual interest rate, to be paid back over 30 years.
First, you'll need to input the interest rate. The HP12C requires the monthly interest rate, not the annual rate. To get the monthly rate, you'd divide 4% by 12 (since there are 12 months in a year). So, enter 4, press the division key (÷), enter 12, and then press the equals key (=). This gives you the monthly interest rate.
Next, you'll input the number of periods, which is the number of months in the loan term. Since it's a 30-year loan and each year has 12 months, you'd multiply 30 by 12. So, enter 30, press the multiplication key (x), enter 12, and then press the equals key (=). This gives you the total number of periods (or payments).
Now, we'll calculate the "amortization of $1". On the HP12C, press the PMT key. This gives you the monthly payment per dollar of loan.
Lastly, you'll multiply the "amortization of $1" by the total amount of the loan to find your actual monthly payment. So, enter the loan amount (200,000 in this case), press the multiplication key (x), and then input the result from step 3, and press the equals key (=). This gives you the monthly payment for the $200,000 loan.
Remember that the HP12C uses Reverse Polish Notation (RPN), which means you enter the numbers first, then the operation. So the sequence for step 1, for example, would be "4 ENTER 12 ÷". It's a different way of thinking, but it can be very efficient once you get the hang of it.
"Wit & Whimsy with the Dumb Ox: Unlocking Knowledge with Rhyme:"
In the world of loans so small, a term you'll want to know,
Amortization of a buck, is how you pay what's owed.
With time and payments set in place, just like a mortgage grand,
Both interest and principal, are paid as you have planned.
You borrow just a dollar, from a friend who's rather kind,
Amortization takes its course, a dollar you'll unwind.
Each month a payment made, with interest if there's some,
Until the day the dollar's paid, and your debt is overcome.
So when you study real estate, and terms you'll need to learn,
Remember Amortization, even for a dollar's turn!