Loan Calculator

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Loan Amount: $

Interest Rate: %

Number of Months:

Answer:

Monthly Payment = $

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Calculator Use

Use this loan calculator to determine your monthly payment, interest rate, number of months or principal amount on a loan. Find your ideal payment by changing loan amount, interest rate and term and seeing the effect on payment amount.

You can also create and print a loan amortization schedule to see how your monthly payment will pay-off the loan principal plus interest over the course of the loan.

Loan Amount: The original principal on a new loan or principal remaining on an existing loan.
Interest Rate: The annual nominal interest rate, or stated rate of the loan.
Number of Months: The number of payments required to repay the loan.
Monthly Payment: The amount to be paid toward the loan at each monthly payment due date.
Compounding: This calculator assumes interest compounding occurs monthly as with payments. For additional compounding options use our Advanced Loan Calculator.

Loan Calculations

When you take out a loan, you must pay back the loan plus interest by making regular payments to the bank. So you can think of a loan as an annuity you pay to a lending institution. For loan calculations we can use the formula for the Present Value of an Ordinary Annuity:

$ PV=\dfrac{PMT}{i}\left[1-\dfrac{1}{(1+i)^n}\right] $

PV is the loan amount
PMT is the monthly payment
i is the interest rate per month in decimal form (interest rate percentage divided by 12)
n is the number of months (term of the loan in months)

Calculation Options

Find the Loan Amount

To calculate the loan amount we use the loan equation formula in original form:

$ PV=\dfrac{PMT}{i}\left[1-\dfrac{1}{(1+i)^n}\right] $

Example: Your bank offers a loan at an annual interest rate of 6% and you are willing to pay $250 per month for 4 years (48 months). How much of a loan can to take?

Solve using CalculatorSoup Loan Calculator

Calculation: Find the Loan Amount
Interest Rate: % 6
Number of Months: 48
Monthly Payment: $ 250

Answer Link: Find the Loan Amount is $10,645.08

Solve using the formula:

PMT = 250
n = 48
i = 0.06/12 = 0.005

$ PV=\dfrac{250}{0.005}\left[1-\dfrac{1}{(1+0.005)^{48}}\right] $

= $10,645.08

Solve on a TI BA II Plus

Be sure P/Y is set to 12 for monthly payments (12 payments per year and monthly compounding).
Press the [2nd] key and the [FV] key to clear the TVM worksheet

Input -250 and press the [PMT] key
(the 250 payment will be negative cash flow for you)
Input 48 and press the [N] key
Input 6 and press the [I/Y] key
Press the [CPT] key and the [PV] key

The answer is: PV = 10,645.08, the loan amount you can get, positive cash flow for you now.

Find the Number of Months

To find the number of months we solve the equation for n:

$ n=\dfrac{ln\left[\dfrac{\frac{PMT}{i}}{\frac{PMT}{i}-PV}\right]}{ln(1+i)} $

Find the Monthly Payment

To find the monthly payment we solve the equation for PMT:

$ PMT=\dfrac{PVi(1+i)^n}{(1+i)^n-1} $

Find the Interest Rate

Finding the interest rate is a complex calculation involving the Newton-Raphson Method which you can read about at MathWorld.

Cite this content, page or calculator as:

Furey, Edward "Loan Calculator" at https://www.calculatorsoup.com/calculators/financial/loan-calculator.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: December 11, 2023

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