# Loan Payment Calculation

Here is a calculator that you can use to compute the monthly payment of a loan. For example, for a \$5000 loan, what is the monthly payment for a loan at 10% interest for 2 years. The principal amount is 5000, there are 12 payments per year if the loan is paid monthly, and a two year loan has 24 monthly payments in total. The calculated payment will be about \$230.72 plus fractional cents that all banks will always round up to the next higher cent.

Some banks will charge you more than this amount because the compute the montly payment per thousand borrowed, round it up to the nearest cent and put it in a table to make life simple for the loan officer who then multiplies this rounded figure by the number of thousands you are borrowing. This will usually add a few additional cents to the monthly payment.

 M = P   i -----   1-(1+i)-N

where the annualized percent interest rate is divided by 100 to get the decimal interest rate and further divided by the payments per year to get periodic interest rate i

Also computed is the total cost which is the monthly payment times the total number of payments. The total interest paid over the life of the loan is the total cost minus the original amount that was borrowed.

 1 Enter the Principal Amount 2 Enter the interest rate as a yearly percentage rate 3 Enter payments per year 4 Enter total number of payments 5 Calculated Payment 6 Total Cost 7 Total Interest

# Loan Term Calculation

Given a payment, a principal mount, and an interest rate, how long will it take to pay off the the loan? It the result is infinity, then you will never get out of debt. If the result is not an integer, usually this is the case, then there will need to be one more payment (over the integer portion of the answer below), which will be for less than the full payment amount, to pay off the loan. The following formula is used to compute the number of payments.

 n = - Log ( i + 1 )  ( 1 - i  P   ---  Pmt ) where i is the decimal annualized interest rate divided by the payments per year

For example, if the payment is 230.72, the interest rate is 10%, and the payments are made every two weeks so there are 26 payments per year, it will take 23 payments to complete the loan and the last payment will be smaller than \$230.72. The total cost of the loan will be less than

\$230.72  *  26 = \$53065.56

which is more than 1 payment or \$230.72 in savings over the example loan above. Naturally, for a 30 year mortgage, the results would be much more dramatic.

 1 Enter the Principal Amount 2 Enter the interest rate as a yearly percentage rate 3 Enter payments per year 4 Enter the payment amount 5 Computed number of payments

# Interest Rate Calculations

There is no closed form solution to find the interest rate given the other parameters. An iterative approach can be used to find the interest rate and it is used in the calculator below. For example, if the monthly payment is \$230.72463168, the term is 24 months, and the principal amount is \$5000, the annualized interest rate is 10%. There are 12 payments per year for monthly payments.

This calculator can also be used to find the equivalent interest rate of a loan with upfront charges. From the first calculator above, a 15 year \$200000 loan at 8 percent has a monthly payment of 1911.304168660713. If the loan required 3 points to be paid up front (a point is 1 percent of the loan), the real loan is for a principal amount reduced by this charge. Using this calculator with a principal of 200000 - ( 3% of 200000 ) = 194000 will give an equivalent interest rate of 8.508 %. Thus, this loan costs more than a no points loan of 8.5% and requires the availability of the \$6000 to pay the points.

 1 Enter the Principal Amount 2 Enter total number of payments 3 Enter payments per year 4 Enter the payment amount 5 Computed annual percentage rate 6 Inerations to convergence

Disclaimer: Before using these pages to make financial decisions, be warned that while these equations and calculators have been checked to varying degrees, the checks are not extensive. It is up to the user to verify formulas and their appropriateness to any particular purpose, and that the formulas have been implemented correctly in the calculators. Errors can also be introduced if the formulas are not used correctly. Additionally errors and malfunctions may be introduced in the calculators at the client side including the browser, which actaully runs the javascript code, the network, the OS or the hardware - all beyond the control of this website. In other words, there's no warrenty on anything. This includes the availability of this site at any particular time.

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