# Calculate Loan Payments and Costs: Formulas and Tools

1743 ## Calculate Loan Payments and Costs: Formulas and Tools

When borrowing money, the required monthly payments are typically a primary concern. Is the loan affordable, given your income and other monthly expenses? If you’re not sure how much you’ll need to pay, a loan payment calculator—or a bit of math—can help you get the answers you need.

Calculators are great for getting a quick answer. They also make it easy to do what-if calculations, which help you truly understand your loan and how your decisions affect your finances. For example, you can compare what happens if you borrow slightly less, or what happens when you get a lower interest rate.

#### Different Loans, Different Calculations

Before you start calculating payments, you need to know what type of loan you’re using. You use a different calculation (or calculator) for different loans. For example, with interest-only loans, you don’t pay down any debt in the early years—you only “service” the loan by paying interest. Other loans are amortizing loans, where you pay down the loan balance over a set period (such as a five-year auto loan).

Use a basic loan calculator: For most home and auto loans this Google Sheets calculator will handle the math for you, so you don’t have to do calculations manually.

Build a spreadsheet: You can also build more advanced spreadsheets in programs like Google Sheets and Microsoft Excel to do the calculations and show you how the loan works year-by-year. See more details about using a spreadsheet for standard amortizing loans (including auto loans, home loans, and personal loans).

If that doesn’t work, don’t worry—we’ll cover several other payment calculations here as well.

#### Formula for Amortizing Loan Payment

This formula works for most amortizing loans, which covers most loans—except credit cards and interest-only loans.

Loan Payment = Amount / Discount Factor or P = A / D

You need the following values:

• Number of Periodic Payments (n) = Payments per year times number of years
• Periodic Interest Rate (i) = Annual rate divided by number of payment periods
• Discount Factor (D) = {[(1 + i) ^n] – 1} / [i(1 + i)^n]

Example: Loan Payment Calculation

Assume you borrow \$100,000 at 6 percent for 30 years, to be repaid monthly. What is the monthly payment?

• n = 360 (30 years times 12 monthly payments per year)
• i = .005 (6 percent annually expressed as .06, divided by 12 monthly payments per year—learn how to convert percentages to decimal format)
• D = 166.7916 ({[(1+.005)^360] – 1} / [.005(1+.005)^360])
• P = A / D = 100,000 / 166.7916 = 599.55

The monthly payment is \$599.55. Check your math with an online payment calculator.

#### Interest-Only Loan Payment Calculation Formula

The loan payment calculation for an interest-only loan is easier. Multiply the amount you borrow by the annual interest rate. Then divide by the number of payments per year. There are other ways to arrive at that same result.

Example (using the same loan as above): \$100,000 times .06 = \$6,000 per year of interest. 6,000 divided by 12 equals \$500 monthly payments.

Assuming you never make additional payments to reduce the principal balance, your monthly payment will remain the same. However, you will have to pay off that loan someday. For example, you may have to start making amortizing payments after the first ten years, or you may need to make a balloon payment at some point to get rid of the debt.

#### Credit Card Payment Calculations

Credit cards are also fairly simple. Lenders typically use a formula to determine your minimum monthly payment. For example, your card issuer might require that you pay at least 3 percent of your outstanding balance each month, with a minimum of \$25 (whichever is more). Of course, it’s wise to pay more than the minimum, but that’s the amount you have to pay to stay out of trouble.

Example: Assume you owe \$7,000 on your credit card. Your minimum payment is calculated as 3 percent of your balance:

• Payment = MinRequired x Balance
• Payment = .03 x \$7,000
• Payment = \$210

Check your math with the Credit Card Payment Calculator on Google Sheets.

But what happens the following month? Your credit card charges interest each month, and you might spend more on your card after you make a payment. In many cases, the same minimum applies: A percentage of your total loan balance is due.

For more details, see a tutorial on calculating your card payments and how each payment affects your balance.

#### Interest and Total Loan Cost

Your monthly payment is certainly important. If you don’t have the cash flow for payments, you can’t afford to buy. But the payment shouldn’t be the only important part of the deal. It’s often more important to focus on:

• The purchase price
• The amount you’ll pay in interest over the life of your loan
• Fees you pay to borrow money

Big picture: Those three components combined make up the total cost of whatever you’re buying. But it’s hard to understand exactly how much you pay when you have several offers from different sources—that’s where the calculations above come in handy. For example, the amortization calculator mentioned above adds up the lifetime interest cost of your loan, and shows you how much you spend on interest every month.

APR: Annual percentage rate (APR) is another useful tool for comparing loan costs. On mortgages, APR accounts for up-front costs (closing costs) in addition to the interest rate you pay on your loan balance. As a result, you get closer to an apples-to-apples comparison among lenders. But the lowest APR isn’t always the best loan, and the calculations above can tell you why. As a rule of thumb, high up-front transaction fees do less damage for loans you keep for a long time.