How to Calculate Monthly Payments on an Amortized Loan

An amortized loan is a type of loan that requires the borrower to make regular payments that are applied to both the principal and interest. The interest amount decreases as the principal amount decreases over time. This means that the borrower pays less interest over the life of the loan compared to other types of loans.

But how do you calculate the monthly payments on an amortized loan? What factors affect the amount of each payment? And how can you use an amortization schedule to plan your repayments? In this article, we will answer these questions and more.

The Formula for Monthly Payments on an Amortized Loan

The formula for calculating the monthly payments on an amortized loan is:

Monthly Payment = (Loan Amount x Monthly Interest Rate x (1 + Monthly Interest Rate)^Number of Months) / ((1 + Monthly Interest Rate)^Number of Months - 1)

This formula may look complicated, but it is actually derived from a simple concept: the present value of an annuity. An annuity is a series of equal payments made at regular intervals. The present value of an annuity is the sum of all the payments discounted to their present value using a certain interest rate.

An amortized loan can be seen as an annuity, where the borrower pays a fixed amount every month to the lender. The lender then discounts these payments to their present value using the interest rate of the loan. The present value of these payments is equal to the loan amount.

Therefore, by rearranging the formula for the present value of an annuity, we can get the formula for the monthly payment on an amortized loan.

An Example of Monthly Payments on an Amortized Loan

Let’s say you want to borrow $10,000 for 5 years at an annual interest rate of 6%. How much will you have to pay every month?

First, we need to convert the annual interest rate to a monthly interest rate by dividing it by 12. This gives us 0.005 or 0.5%.

Next, we need to find out how many months are in 5 years by multiplying it by 12. This gives us 60 months.

Then, we can plug these numbers into the formula for monthly payments on an amortized loan:

Monthly Payment = ($10,000 x 0.005 x (1 + 0.005)^60) / ((1 + 0.005)^60 - 1)

Monthly Payment = ($10,000 x 0.005 x 1.34885) / (0.34885)

Monthly Payment = $193.33

Therefore, you will have to pay $193.33 every month for 5 years to repay your $10,000 loan.

How to Use an Amortization Schedule

An amortization schedule is a table that shows how each monthly payment on an amortized loan is split between principal and interest, and how much balance remains after each payment.

An amortization schedule can help you understand how your loan works and how much interest you will pay over time. It can also help you plan your budget and decide whether you want to pay off your loan early or refinance it.

You can create an amortization schedule using a spreadsheet software like Excel or Google Sheets, or use an online calculator like this one.

Here is an example of an amortization schedule for the $10,000 loan we used earlier:

As you can see, the principal portion of each payment increases while the interest portion decreases over time. The balance also decreases until it reaches zero at the end of the loan term.

An amortized loan is a type of loan that requires the borrower to make regular payments that are applied to both the principal and interest. The formula for calculating the monthly payments on an amortized loan is based on the present value of an annuity. An amortization schedule can help you understand how your loan works and how much interest you will pay over time.

FAQs

Q: What is the difference between an amortized loan and a balloon loan?

A: A balloon loan is a type of loan that requires the borrower to make small payments for a period of time, and then pay a large lump sum at the end of the loan term. A balloon loan is not fully amortized, meaning that the payments do not cover the entire principal and interest. A balloon loan may have a lower interest rate than an amortized loan, but it also carries a higher risk of default.

Q: What is the difference between an amortized loan and a revolving debt?

A: A revolving debt is a type of debt that allows the borrower to borrow and repay money repeatedly, up to a certain limit. A revolving debt does not have a fixed payment schedule or a fixed interest rate. A revolving debt may offer more flexibility than an amortized loan, but it also may have higher fees and interest charges.

Q: How can I save money on interest on an amortized loan?

A: There are several ways to save money on interest on an amortized loan, such as:

• Making extra payments or paying more than the minimum amount every month. This will reduce the principal amount faster and lower the interest charges.
• Refinancing your loan to get a lower interest rate or a shorter loan term. This will reduce the total amount of interest you will pay over time.
• Choosing a loan with no prepayment penalty or fees. This will allow you to pay off your loan early without any additional costs.

Q: How can I find out how much I owe on my amortized loan?

A: You can find out how much you owe on your amortized loan by looking at your most recent statement from your lender, or by contacting them directly. You can also use an online calculator like this one to estimate your remaining balance and payments.

Q: How can I create my own amortization schedule?

A: You can create your own amortization schedule using a spreadsheet software like Excel or Google Sheets, or use an online calculator like this one. To create your own amortization schedule, you will need to know your loan amount, interest rate, and loan term. You will also need to use some formulas to calculate the monthly payment, principal, interest, and balance for each period.