Calculate Interest Payments
Not all loans are created equal. Understanding how to calculate a monthly payment, as well as the amount of interest you'll pay over the life of the loan, are very helpful in choosing the perfect loan for you. Understanding exactly how the money adds up can requires you to work with a complex formula, but you can also calculate interest more simply using Excel.
Contents
Steps
Quickly Comprehending Your Loan
- Input your loan information into an online calculator to quickly determine your interest payments. Calculating interest payments is not a simple equation. Luckily, a quick search for "interest payment calculator" makes it easy to find your payment amounts as long as you know what to input into the calculator:
- Principal: The amount of your loan. If you loan is $5,000, the principal is $5,000.
- Interest: In simple terms, the percentage of money you're being charged to have the loan. It is either given as a percentage (such as 4%) or a decimal (.04).
- Term: Usually in months, this is how long you have to pay the loan off. For mortgages it is often calculated in years.
- Payment Option: Almost always a "fixed-term loan." However this can be different for specialty loans. Ask if the interest and payment schedule is fixed before getting a loan if you are unsure.^{[1]}
- Find out your interest rate before getting a loan. The interest rate is the cost you pay for borrowing money. It is the rate of interest that you will pay on the principal for the life of the loan. You want it to be as low as possible, as even .5% of a difference can mean a huge sum of money.^{[2]} If you would prefer lower payments, you may pay a higher interest rate and more total interest over the loan, but less each month. Someone with less savings on hand or whose income is bonus or commission-based would likely prefer this option. However, want to stay below 10% interest whenever possible. The common rates for different loans are:
- Auto: 4-7% ^{[3]}
- Home: 3-6%
- Personal Loans: 5-9%
- Credit Cards: 18-22% This is why you should avoid large purchases you can't repay quickly on credit cards.
- Payday Loans: 350-500% These loans are very dangerous if you can't pay them off within 1-2 weeks.^{[4]}
- Ask about accrual rates to determine when you get charged interest. In technical terms, the accrual rate tells you how often lender calculates the interest you owe. The more frequently you're charged the more you owe, since you have less time to pay off and the bill and prevent higher interest.^{[5]} Look, for example, at a $100,000 loan with 4% interest, compounded three different ways:
- Yearly: $110,412.17
- Monthly: $110,512.24
- Daily: $110,521.28
- Use longer term loans to pay less each month, but more overall. The term is the period of time that you have to repay the loan.^{[6]} Again, this will vary from one loan to the next, and you'll need to choose a loan with a term that meets your needs. A longer term will typically result in more interest paid over the life the loan, but smaller monthly payments.^{[4]} For example, say you have a $20,000 auto loan with 5% interest. Total payment would be:
- 24 Month Term: You pay $1,058.27 in total interest, but only $877.43 each month.
- 30 Month Term: You pay $1,317.63 in total interest, but only $710.59 each month.
- 36 Month Term: You pay $1,579.02 in total interest, but only $599.42 each month.^{[1]}
Calculating your Payment by Hand
- Learn the formula for complex interest payments. Calculating your payments and interest requires the use of a mathematical formula, which is as follows: <math> Payment = Principal * \frac{i(1+i)^n}{(1+ i)^n - 1}</math>^{[7]}
- The "i" represents interest rate, and the "n" represents the number of payments.
- Like most equations in finance, the formula for determining your payment is much more intimidating than the math itself. Once you understand how to set up the numbers, calculating your monthly payment is as easy as pie.
- Adjust for frequency of payments. Before you plug numbers into the equation, you must adjust your interest payment “i” for how often you are paying.
- For example, imagine you took out a loan at 4.5 percent, and the loan required you to make payments on a monthly basis.
- Since your payments are monthly, you will need to divide the interest rate by 12. 4.5 percent (.045) divided by 12 equals 0.00375. Plug this number in for "i."^{[7]}
- Adjust for number of payments. To determine what to plug in for "n," your next step is to determine the total number of payments you'll be making over the term of the loan.
- Imagine that your monthly payments are on a loan with a 30 year term. To find the number of payments, simply multiply 30 by 12. You'll be making 360 payments.^{[7]}
- Calculate your monthly payment. To figure your monthly payment on this loan, it is now just a matter of plugging the numbers into the formula.This might look intimidating, but if you go step by step, you'll soon have your interest payment. Below are the steps of the calculation, done one by one.
- Continuing with the example above, imagine you have borrowed $100,000. Your equation will look like this: <math>100,000 * \frac{0.00375 (1 + 0.00375)^360}{(1 + 0.00375)^360 - 1}</math>
- <math>100,000 * \frac{0.00375 (1.00375)^360}{(1 + 0.00375)^3600 - 1}</math>
- <math>100,000 * \frac{0.00375 (3.84769....)}{(1 + 0.00375)^360 - 1}</math>
- <math>100,000 * \frac{0.01442..... }{(1 + 0.00375)^360 - 1}</math>
- <math>100,000 * \frac{0.01442..... }{(1.00375)^360 - 1}</math>
- <math>100,000 * \frac{0.01442..... }{3.84769..... - 1}</math>
- <math>100,000 * \frac{0.01442..... }{2.84769.....}</math>
- <math>100,000 * 0.00506685..... = 506.69</math>
- $506.69. This will be your monthly payment.
- Calculate your total interest. Now that you have the monthly payment, you can determine how much interest you will pay over the life of the loan. Multiply the number of payments over the life of the loan by your monthly payment. Then subtract the principal amount you borrowed.^{[7]}
- Using the example above, you'd multiply $506.69 by 360 and get $182,408. This is the total amount you'll pay over the loan's term.
- Subtract $100,000 and you end up with $82,408. That is the total amount of interest you'd pay on this loan.
Calculating your Interest with Excel
- Write down the principal, term ,and interest from your loan in one column. Fill separate boxes with the amount of the loan, the length you have to pay, and the interest, and Excel can calculate your monthly payments for you. For the remainder of the section, you can use the following example loan:
- You take out a $100,000 home loan. You have 30 years to pay it off at 4.5% annual interest rate.
- Write the principal in as a negative number. You need to tell Excel that you're paying a debt. To to so, write the principal with a negative number, without the $ sign.
- -100,000 = Principal
- Determine the number of payments you're making. You can leave it in years, if you want, but your answer would spit out yearly interest payments, not monthly. Since most loans are paid monthly, simply multiple the number of years by 12 to get your total number of payments. Write this down in another box.
- -100,000 = Principal
- 360 = Number of Payments
- Convert your interest rate to fit the number of payments. In this example, your interest rate is annual, meaning it is calculated at the end of the year. However, you're paying monthly, meaning you need to know what your monthly interest rate is. Since 4.5% is for 12-months of interest, simply divide by 12 to get one month's worth of interest. Be sure to convert the percentage to a decimal when you're done.
- -100,000 = Principal
- 360 = Number of Payments
- <math>\frac{4.5%}{12} = .375% =</math><math> .00375</math> = Monthly interest.
- Use the =PMT function to determine interest payments. Excel already knows the equation for calculating monthly payments, with interest. You just have to give it the information it needs to make the calculation. Click on an empty box, then ;locate the function bar. It is located right above the spreadsheet and labeled "fx." Click inside of it and write "=PMT("
- Do not include the quotation marks.
- If you're Excel savvy, you can set up Excel to accept the
- Enter the inputs in the correct order. Place the values needed to calculate the payment in the parenthesis, separated by commas. In this case, you'll enter (Interest rate,number of periods,principal ,0).
- Using the example above, the full entry should read: "=PMT(0.00375,360,-100000,0)"
- The last number is a zero. The zero indicates you will have a balance of $0 at the end of your 360 payments.
- Make sure you remember to close the parenthesis off.
- Press enter to get your monthly payment. If you've entered the function correctly, you should see your total monthly payment in =PMT cell of the spreadsheet.
- In this case, you'll see the number $506.69. That will be your monthly payment.
- If you see "#NUM!" or some other output that doesn't make sense to you in cell, you've entered something incorrectly. Double check the text in the function bar and try again.
- Figure out the total payment amount by multiplying by your number of payments. To figure out the total amount you will pay over the life of your loan, all you have to do is multiply the payment amount by the total number of payments.
- In the example, you'd multiply $506.69 by 360 to get $182,408. This is the total amount you'll pay over the loan's term.
- Figure out how much you pay in interest by subtracting the principal from your total. If you want to know how much interest you'll pay over the term of the loan, this is just a matter of subtraction. Subtract the principal from the total amount you'll pay.
- In the example you'd subtract $100,000 from $182,408. You end up with $82,408. This is your total interest paid.
Reusable Spreadsheet to Calculate Interest Payments
The following table details how to use Excel, Google Docs, or similar spreadsheet programs to calculate simply interest payments on anything. Simply fill it in with your own numbers. Note that, where it says <math> Fx = </math>, you must fill this part in the upper bar of the spreadsheet labeled "Fx." The numbers (A2, C1, etc.) correspond to the boxes as they are labeled in Excel and Google Docs.
A | B | C | D | |
---|---|---|---|---|
1 | [Principal] | [Number of Payments] | [Interest] | [Interest per Month] |
2 | Negative Loan Amount (-100000) | Total number of payments, in months. (360) | Your interest rate, as a decimal. (.05) | Your monthly interest rate (divide yearly interest by 12) |
3 | Monthly Payment | FX=PMT(D2,B2,A2,0). NOTE: The final digit is the number zero. | ||
4 | Total Money Owed | FX=PRODUCT(D3,B2) | ||
5 | Amount Paid in Interest | FX=SUM(D4,A2) |
Tips
- Understanding how to calculate your loan payments will give you the tools you need to weed out deals that aren’t just good, but are good for you.
- If you are experiencing sporadic cash-flow and value a loan that isn’t necessarily the lowest cost but offers lower and less-frequent payments, a longer term loan may be a better choice, even thought the interest will be greater in the long run.
- If you have more savings than you need and are interested in finding the lowest cost product to fulfill your needs, a loan with a shorter term and higher payments will mean less interest and might be right for you.
Warnings
- There are often times when the lowest rate advertised is not the lowest cost loan. When you understand how to the pieces to pricing these deals work, you can quickly understand the true “cost” of the debt versus the incremental price your paying for some of the features.
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Sources and Citations
- ↑ ^{1.0} ^{1.1} http://www.interest.com/home-equity/calculators/monthly-payment-calculator/
- http://www.investopedia.com/terms/i/interestrate.asp
- http://www.bankrate.com/finance/auto/current-interest-rates.aspx
- ↑ ^{4.0} ^{4.1} http://econlib.org/library/Enc/InterestRates.html
- http://www.investopedia.com/terms/a/accrual-rate.asp
- http://www.investopedia.com/terms/t/term.asp
- ↑ ^{7.0} ^{7.1} ^{7.2} ^{7.3} http://www.fonerbooks.com/interest.htm