How To Calculate A Monthly Payment On A Loan (2024)
When you use an installment loan, you’ll repay the amount you’ve borrowed (the principal) over a set amount of time (the repayment term). You’ll also have to pay interest and fees, both of which make up the loan’s annual percentage rate (APR).
The principal, loan term and APR are the three main components of your monthly payment. And by knowing each, you’ll be able to calculate how much your installments will be using a loan calculator or a mathematical formula. We’ll explain the math below, but you can also use our Simple Loan Calculator to get an idea of your monthly payment.
Monthly Loan Payment Formula
Depending on the type of personal loan you choose, you can use three formulas to determine the monthly payment. Before you can use a formula, you’ll need to know the loan type and the variables mentioned above. They’ll be represented by the following:
P: The loan’s principal or the total amount of money you’ve borrowed
r: The loan’s APR or the annual rate (the APR spread over 12 months)
n: The number of payments you’ll make over a specific time frame
Interest-Only Loans
An interest-only loan uses a period at the beginning of the term when the borrower only pays interest. After the interest-only period ends, the borrower will pay the principal in installments or as a single lump sum.
Interest-only personal loans are rare, but if you end up using this option, you can calculate the monthly interest payment with this formula:
Again, “P” represents your principal amount, and “r” is your APR. However, “n” in this equation is the number of payments you’ll make over a year.
Now for an example. Let’s say you get an interest-only personal loan for $10,000 with an APR of 3.5% and a 60-month repayment term. You can use the following steps to calculate your interest-only monthly payment:
Multiply the principal by the APR. Take $10,000 and multiply it by your APR, 3.5%. You should get $350 as your annual interest amount.
Divide your annual interest by the number of payments. Divide $350 by the number of payments you’ll make in a year. For this scenario, you’ll make 12 payments. You should get $29.17 as your interest-only monthly payment.
Amortizing Loans
Unlike an interest-only loan, an amortizing loan payment goes toward both the interest and principal amount. That means you’ll be paying off the loan in equal monthly installments over the repayment term.
The formula for calculating the monthly payment on an amortizing personal loan is:
Monthly Payment = P ((r (1+r)n) ∕ ((1+r)n−1))
Let’s use the previous example, but this time, the personal loan you get is amortizing. The principal (P) is $10,000, the APR is 3.5% and you have a 60-month repayment term (n). With this formula, “r” stands for the annual rate, not the APR. You can use these steps to find the monthly payment:
Divide your APR by 12 months to get your annual interest rate (r). Divide 0.035 by 12 to get 0.002917.
Fill out the formula. You can now plug your loan information into the above equation. You should have $10,000((0.002917(1+0.002917)60) ∕ ((1+0.002917)60−1)).
Solve the equations inside the first set of parentheses. You should end up with $10,000((0.002917 × 1.00291760) ∕ (1.00291760−1).
Solve the exponentials. Calculate 1.00291760 to get 1.190967. The formula is now $10,000((0.002917 × 1.190967) ∕ (1.190967−1)).
Solve the equations in the second set of parentheses. First, multiply 0.002917 by 1.190967 to get 0.003474. Then you can subtract 1 from 1.190967 to get 0.190967 for the other half of the equation. Your formula should look like $10,000(0.003474 ∕ 0.190967).
Divide the numbers in the final set of parentheses. Take 0.003474 divided by 0.190967 to get 0.018192.
Multiply the loan principal by the total. You will then multiply $10,000 by 0.018192 to get your monthly payment, $181.92.
At this point, you can also use a loan calculator to make an amortization schedule for your loan. This extra step can help you visualize how your loan will be repaid over the length of the term.
The formula is: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1], where M is the monthly payment, P is the loan amount, i is the interest rate (divided by 12) and n is the number of monthly payments.
The lending institution has offered a loan with an annual interest rate of 7.2% for a tenure of 10 years. EMI = Rs 10,00,000 * 0.006 * (1 + 0.006)120 / ((1 + 0.006)120 – 1) = Rs 11,714. Hence, you will be paying the EMI of Rs 11,714 every month for 10 years.
The monthly payment on a $3,000 personal loan will depend on the loan term and the interest rate. For example, the monthly payment on a two-year $3,000 loan with an annual percentage rate (APR) of 12% would be $141.22. The monthly payment on a $3,000 loan with a six-year term and an APR of 12% would be $58.65.
To calculate simple interest monthly, we have to divide the yearly interest calculated by 12. So, the formula for calculating monthly simple interest becomes (P × R × T) / (100 × 12).
Use the formula P (r(1+r)^n)/((1+r)^n-1) to calculate your payment for each month. “P” is the amount of the loan (which is called the principal), “r” is your interest rate, and “n” is your number of payments.
You can calculate your EMI amount with the help of the mathematical formula given below: EMI Amount = [P x R x (1+R)^N]/[(1+R)^N-1] where P, R, and N are the variables. It also means that the EMI value will change every time you change any of the three variables. 'P' stands for the 'Principal Amount'.
you need to input details like the amount borrowed, interest rate, and loan tenure to calculate your monthly EMI. the formula used is: EMI = [p x r x (1+r)^n]/[(1+r)^n-1]
For example, if you currently owe $500 on your credit card throughout the month and your current APR is 17.99%, you can calculate your monthly interest rate by dividing the 17.99% by 12, which is approximately 1.49%.Then multiply $500 x 0.0149 for an amount of $7.45 each month.
Again, “P” represents your principal amount, and “r” is your APR. However, “n” in this equation is the number of payments you'll make over a year. Now for an example. Let's say you get an interest-only personal loan for $10,000 with an APR of 3.5% and a 60-month repayment term.
For example, if you have a $20,000 line of credit with a 6 percent APR and an interest-only repayment period of 10 years, you will multiply the amount you borrowed by your interest rate. This would show your annual interest costs. You then divide that figure by 12 months to determine your monthly payment.
A $20,000 loan at 5% for 60 months (5 years) will cost you a total of $22,645.48, whereas the same loan at 3% will cost you $21,562.43. That's a savings of $1,083.05. That same wise shopper will look not only at the interest rate but also the length of the loan.
Divide the interest rate you're being charged by the number of payments you'll make each year, usually 12 months.Multiply that figure by the initial balance of your loan, which should start at the full amount you borrowed.
For loans, the PMT function in XLS can be used to calculate the monthly payment. The mathematical formula for this PMT function is P = (Pv*R) / [1 - (1 + R)^(-n)] . P = Monthly Payment. Pv = Present Value (starting value of the loan) APR = Annual Percentage Rate.
For example, if your interest rate is 6 percent, you would divide 0.06 by 12 to get a monthly rate of 0.005. You would then multiply this number by the amount of your loan to calculate your loan payment. If your loan amount is $100,000, you would multiply $100,000 by 0.005 for a monthly payment of $500.
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