# Loan Calculator

Created by Davide Borchia
Last updated: Jul 03, 2022

If you are wondering how to calculate a loan's payments, you are in the right place. Here you will learn:

• What is a loan;
• The elements of a loan;
• Additional elements of a loan (fees and obligations);
• How to calculate the monthly loan payments; and
• How to use our loan payment calculator.

We have other tools that can be helpful with your funds: try our velocity of money calculator and our mortgage calculator.

## Elements of a loan

A loan is uniquely identified by a set of fundamental quantities. To calculate your loan payments properly, be sure to know all of them.

• Loan amount - The loan amount is the amount of money you ask the lender for. The final amount of money received may disagree with the requested one due to commissions or fees.
• The nominal interest rate is the amount of money you pay on your loan.
• The annual percentage rate (APR) considers fees and commissions other than the interest. This is the true amount of money you will pay to the lender.
• Compounding frequency - the frequency used by the lender to calculate the loan's interest on the principal loan amount. To understand this concept better, check the compound interest calculator.
• Loan term - The time in which you are obliged to fulfil all your payments.
• Payment frequency - The frequency of your payments. It can be monthly, bi-weekly, weekly, or quarterly.

## Additional elements of a loan

• Prepaid fees - Fees without interest you have to pay in the moment you subscribe to the loan, or at the end of the payments.
• Loaned fees - Fees with an interest, added to the amount of the principal. They affect more the resulting APR.
• Origination fee - The fee you owe the lender for the subscription of the loan. The value of the fee depends on many factors (the type of loan, the principal, your credit score, etc.) and can be paid:
• From the principal: you will receive a lower amount of money than the one you required.
• As a loaned fee: you will include the origination fee in the principal, paying interests over it.
• Out of pocket: this payment method won't affect the loan.

## How to use our loan calculator

When subscribing to a loan, you know some (of all) the parameters we listed above.

Start inserting them into our calculator. First, choose whether you know the interest rate, APR, or both. This will change the output of our loan payment calculator. Insert the values of these quantities in the appropriate fields.

Choose the compound frequency. If you don't know it, a safe bet is to say that it's monthly!

Proceed with the value of the loan itself (the principal) and the term of the loan. Finally, choose the preferred loan payment schedule.

This will be enough for us: we will calculate everything for you. If you need to add the other parameters, go to the second box in the calculator, and fill the fields you need.

## How to calculate a loan's payment

To calculate the regular payment of a loan you can use a simple formula:

$MP=P\cdot\left(\frac{r\cdot (1+r)^n}{(1+r)^n-1}\right)$

Where:

• $MP$ is the monthly payment;
• $P$ is the principal;
• $r$ is the monthly interest rate; and
• $n$ is the number of months in the loan term.

🙋 Our loan calculator uses a slightly different formula to calculate the monthly/regular payments: don't worry if there's a discrepancy between the results we give you and the one you can calculate on your own!

The result of the calculation takes into account both the principal's back payment and the loan's calculated interest.

## What can you learn from our loan paymen?t schedule calculator

In the results box of our loan payment calculator, you will find:

• The total amount of money received at the subscription of the loan;
• The amount of each of your periodic payments;
• How much will you owe to the lender in terms of calculated loan interests and fees without interest (with the appropriate breakdown);
• The value of the fees with interest;
• The total amount you owe to the lender; and
• The APR.

🙋 The results above are referred to calculations performed with the annual interest rate.

If you know the APR, your results may change slightly: here, we can't make up the difference between fees with and without interests, and the breakdown is minimally simplified.

## Visualize the calculated loan payment - schedule and total

The pie chart in our loan payment calculator gives you a breakdown of the total payment percentages. The chart will change according to the type of interest you choose: with the annual nominal interest, you will see an accurate breakdown of each type of fee.

The chart below represents the status of your loan after each payment. You can identify the remaining amount you owe to the lender or the total paid interest, plus, eventually, a breakdown of the fees.

You can also check the same data in a table with monthly or annual frequency.

Davide Borchia
Main specifications
Known rate
nominal interest rate
Interest rate
%
Compound frequency
monthly
Loan amount
$Loan term yrs mos Payment frequency monthly Additional fees Prepaid fee$
Loaned fee
$Origination fee % Origination fee repayment from the loan amount Results You receive a$9,200 loan after deducting the origination fee of $800. Your periodic payment is$169.1, and from this, $8.05 covers the additional fees rolled into the loan. The total interest payment is$1,675.33, and from this, $1,595.55 charged on the loan amount and$79.78 is paid after the additional fees have been rolled into the loan.
The total additional fees with interest charged on them are $1,579.78. The total payment you need to make is$12,375.33; thus, the total finance charge (total interest plus additional fees) is \$3,175.33.
The APR is 10.31%, and the effective APR that accounts for the compounding frequency as well is 10.81%.
Total payment percentage breakdown
Balances
Display in
chart and table
Show balances on
yearly basis
YearOpening balanceYearly principalYearly interestClosing balanceTotal paid
110,426.711,465.88466.718,960.822,229.22
28,883.781,540.88391.717,342.94,258.44
37,261.911,619.71312.885,642.26,287.66
45,557.071,702.58230.013,854.498,316.89
53,7651,789.69142.91,975.3210,346.11
61,881.251,881.2551.34012,375.33
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