# Loan Calculator

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This Post: Loan Calculator

Choose a Calculation Find the Loan Amount Find the Interest Rate Find the Number of Months Find the Monthly Payment

## 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

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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

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(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{lnleft[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.

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