Online Calculator Resource

# Loan Calculator

Loan Calculator

Monthly Payment = $554.74 Create an Amortization Schedule Share this Calculator & Page ## 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

1. Input -250 and press the [PMT] key
(the 250 payment will be negative cash flow for you)
2. Input 48 and press the [N] key
3. Input 6 and press the [I/Y] key
4. 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"; from https://www.calculatorsoup.com - Online Calculator Resource.