Loan Calculator

This is a general purpose loan calculator. You can calculate the payment, amount, interest rate or term (number of payments) at different payment and compounding frequencies.

Please click on the above "Help" button for details.

Other Useful Loan Calculators...

• Amortization schedule — shows how each payment is allocated to principal and interest
• Auto calculator with down payment calculation — asset price less a down payment & calculates loan values. Useful for calculating financing for any asset when downpayments are involved, but particularly good for cars.
• Mortgage calculator with percent down — asset price less a percentage down & calculates loan values. Useful for calculating financing for any asset when downpayments are involved, but particularly good for real estate.
• Balloon payment calculator — this one also accommodates a final balloon payment
• Bridge loan calculator — determines if a bridge loan is needed and what the payment will be
• Extra payment calculator — see how much interest you can save by making regular extra payments

What is the Interest Rate?

You can calculate a loan's "nominal annual interest rate" which is the rate usually quoted by the lender. Use the calculator for confirming the quoted rate. (Just enter a "0" for annual rate.) A discussion of the calculation used to arrive at the nominal annual interest rate, is beyond the intent of this web page. Suffice it to say, it is involved. The "periodic interest rate" is the interest rate for a period — that is, the time between two scheduled payments. The formula for the periodic interst rate is very straight forward.

General Periodic Interest Rate Equation:

Periodic Rate = Annual Rate / Periods Per Year / 100

Example of common periods per year: Annually: 1, Monthly: 12, Weekly: 52 and Daily: 365.

Calculating Loan Payment Equation

Payment = PV * (Periodic Rate / (1 - (1 / (1+
          Periodic Rate))Total Periods))

Calculating Term Equation

S = Pmt * (1.0 + Periodic Rate * Timing)

Term = Log(S / (Periodic Rate * -PV + S)) /
          Log(1.0 + Periodic Rate))

If the first payment is due on the day the loan amount is advanced then timing is set to 1. If the first payment amount is due after the funds are made available, then the timing value is 0.

Calculating Loan Amount Equation

A = (1-(1+Periodic Rate)(- Total Periods+Type) )
          / Periodic Rate

A = Pmt * ( Type + A )

Examples of Solving Common Loan Equations

These days the housing market, in the US, is very weak, and mortgages can be hard to get for those with less than perfect credit. You find yourself in the position where you want to retire, sell your home and move away. You have found a prospective buyer but the buyer is having difficulty obtaining financing. In order to close the sale, you offer him owner financing. The terms for the loan are for an initial mortgage balance of $365,000, payable over fifteen years in 180 monthly payments and the interest rate will be 6.5%. What is the payment amount?

First, calculate the periodic rate.

Periodic Rate = 0.005416667 = 6.5% / 12 / 100

Payment = $3,179.54 = 365,000 * (0.005416667 / (1 - (1/
          (1+0.005416667))180))

Now that you know the payment amount, you can check the accuracy of your calculation by solving for one of the other loan attributes.

S = 3,179.54188 = 3,179.54 * (1.0 + 0.0054167 * 0)

Term = 180.00018 = Log( 3,179.54 /
          (0.0054167*-365,000+3,179.54)) /
          Log(1.0+ 0.0054167))

And the loan amount...

A = 114.796412 = (1-(1+0.0054167)(-180+0) ) / 0.0054167

Loan Amount = 364,999.78 = 3,179.54 * (0+114.796412)

You may wonder why the loan amount is not $365,000. The 0.22 difference is the rounding error. Because a payment amount is not exactly $3,179.54 (but we can't have a payment that includes a fractional cent) the loan amount will not calculate to be exactly $365,000 either.

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