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Often, lenders require that you make monthly or quarterly payments. Therefore, it is more useful to know what the monthly or quarterly payment is, rather than simply the annual payment. Fortunately, the same formula is used, with some minor revisions. For the sake of this example, assume the new loan is the same as previously-discussed one, with the only change being you are now required to make monthly payments for the two year period. Although the formula is largely the same as that for annual payments, a few minor changes occur to reflect the fact that there are now more payments. Again, the standard formula is: Payment=(r(P))(1(1+r)n){\displaystyle Payment={
rac {(r(P))}{(1-(1+r)^{-n})}}} First, the amount of periods in the loan, or "n", would change. Instead of being 2 (representing two years before, or two annual payments), it is now 24 for monthly payments (representing 1 payment a month for 2 years) and 8 for quarterly payments (representing one payment each quarter for the two years). Second, the annual interest rate would need to change to reflect the fact there are more payments. To determine an interest rate for periodic payments, divide the annual interest rate by the number of payments required within a year. For example, a 9% annual interest rate is equivalent to a .0075 or .75% monthly interest rate (.09/12). The new formula, with all the example numbers plugged in looks like this: Payment=(0.0912($10,000))(1(1+0.0912)24){\displaystyle Payment={
rac {({
rac {0.09}{12}}(\$10,000))}{(1-(1+{
rac {0.09}{12}})^{-24})}}} Start by simplifying the rate by solving for the monthly interest rate. This is done by dividing the annual rate of 9% by 12, as in the equation, to get 0.0075. After you do so, your equation should look like this: Payment=(0.0075($10,000))(1(1+0.0075)24){\displaystyle Payment={
rac {(0.0075(\$10,000))}{(1-(1+0.0075)^{-24})}}} Continue by solving the numerator (the top part of the equation). Multiply the two numbers (rate and principal) together to solve this step. Your equation should now look like this: Payment=($75)(1(1+0.0075)24){\displaystyle Payment={
rac {(\$75)}{(1-(1+0.0075)^{-24})}}} Next, simplify the denominator (bottom of the equation) by adding the rate to 1. This comes to 1.0075 in our example. The equation now looks like this: Payment=($75)(1(1.0075)24){\displaystyle Payment={
rac {(\$75)}{(1-(1.0075)^{-24})}}} Next, solve the exponent in the equation by raising the (rate +1) found in the last step to the power of -24. This comes to 0.8358. The equation now looks like this: Payment=$751(0.8358){\displaystyle Payment={
rac {\$75}{1-(0.8358)}}} Simplify by subtracting your result in the last step from one. In our example, this would be 10.8358{\displaystyle 1-0.8358}, which yields 0.1642. At this point, the equation looks like this: Payment=$750.1642{\displaystyle Payment={
rac {\$75}{0.1642}}} Finally, divide the top part of the equation by the bottom to get your monthly payment. In this case, Payment=$456.76{\displaystyle Payment=\$456.76} If necessary, you can convert your monthly payment to an annual total by multiplying it by 12. Here, 12473.78=$5,481.12{\displaystyle 12*473.78=\$5,481.12}. Once again, keep in mind that there are plenty of online calculators available to calculate this online, without ever calculating the payment yourself.
Understand the reason to calculate periodic payments on a loan. Learn the formula for calculating periodic payments on a loan. Fill in the equation with your values. Begin to calculate the periodic payments on the loan. Solve the numerator. Simplify the denominator. Solve the exponent. Simplify the denominator again. Solve for your monthly payment. Convert your answer to an annual payment total. Use an online calculator to confirm results.