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Loan Calculator

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Introduction

Whether you are buying a new home, financing a car, or trying to fund a big personal project, the loan calculator will help you accurately estimate monthly payments, interest rates, and repayment schedules. This will enable you to make better borrowing decisions and take control of your finances.

Loans are financial transactions in which one party who has money, called a lender, lends money to another party who needs money, called the borrower, and charges an interest rate as compensation.

Loans are commonly used by individuals as well as businesses to fund various expenses. People might buy a house or car, fund their education, or even invest in a project. Businesses might use loans to purchase assets, invest in projects, expand existing businesses, etc.

In general, the terms of the loan will include the principal amount (initial sum borrowed), the interest rate (cost of borrowing money), and the repayment period (the repayment duration for the loan).

Above all, properly managing and repaying loans is critical for maintaining financial stability and credit scores.

The Loan Calculator will help you compare loans on different parameters, and you can make a well-informed decision on which one to choose.

How to use the Loan Calculator?

Using the loan calculator, you can calculate the periodic payments that need to be made, the total interest paid, and the total payment, which is the sum of the principal and interest.

The variables in the calculator are:

Principal (P) The interest rate is the cost of a loan

Annual Interest Rate (R) The interest rate advertised by the bank while borrowing the Principal.

Loan Tenure (N) (Years or Months) The period for which the Principal was borrowed.

Compounding Frequency The number of times per year the accumulated interest is paid out could be yearly, half-yearly, quarterly, monthly, weekly, or daily.

Payback Frequency The frequency at which the loan payments are made.

Payment Amount The fixed amount of money to pay every period to repay the loan.

Total Interest Paid The total interest paid back to the lender over the course of the loan.

Total Payment (Principal + Interest) The total amount paid back to the lender.

What is a Loan?

A loan is a financial arrangement where one party lends a certain amount of money or assets to another party. The borrower will repay the lender the original amount borrowed, known as the principal, along with any additional charges, such as interest or financing fees, at a later agreed-upon date.

Basically, a loan involves the temporary transfer of funds from the lender to the borrower, with the expectation that the borrower will reimburse the lender in the future.

Before exchanging money, the borrower and lender agree on the loan’s terms. Furthermore, the lender may ask the borrower to provide collateral, which is a valuable asset that the borrower possesses given to the lender for security, and these conditions will be mentioned in the loan document.

Features of a Loan

A loan will usually have the following primary features.

Principal: This is the initial sum that you borrowed from the lender. It could be $200,000 for your new home or $20,000 for the car you are buying.

Interest Rate: The interest rate is the money the lender charges to borrow the sum. In other words, it is the cost of borrowing the money. The interest rate a lender offers will depend on the borrower’s creditworthiness.

Loan Term: The amount of time the borrower has to repay the loan. Depending on the specific loan type, however, this period can vary, ranging from just a few weeks to several years.

Interest Payments: Borrowers typically make regular repayments to the lender, usually on a monthly basis until the loan is repaid. These monthly payments are often a fixed amount.

Types of Loans

Secured and Unsecured Loans

Secured loans, like mortgages and car loans, require collateral, the asset the borrower purchases will be provided as collateral, such as a home or a vehicle. On the other hand, unsecured loans, like credit cards and signature loans, do not require collateral.

Unsecured loans typically have higher interest rates than secured loans due to the higher risk of default. Lenders may seize the collateral in case of default on secured loans, whereas unsecured loans depend more on the borrower’s credit history and income, leading to varying interest rates.

Personal Loans

Personal Loans are usually unsecured loans that people utilize for various purposes, like funding their weddings, medical expenses, vacations, pricey electronics, home renovations, etc.

Banks, credit unions, and online lenders offer these personal loans, and since they are unsecured, they tend to have higher interest rates. Rates typically range from 6% to 36%, and payments range from 12 – 84 months.

A personal loan would be the best option for someone who only needs to borrow a modest sum of money and is certain they can pay it back within a few years.

The banks provide unsecured personal loans based on the individual’s credit history and creditworthiness.

Secured personal loans are also available, and since the collateral backs them up, lenders consider these types of loans less risky and offer lower interest rates or increase your loan amount.

Student Loans

Student loans are offered to young people looking to pursue higher education and want to finance their studies using a loan. Usually, their parent or relative will cosign the loan as the student will not have a credit history.

The loan may cover the tuition, supplies, books, living costs, and other fees associated with the university. These loans will not cover Non-educational expenses, extracurricular activities, and sometimes study abroad or exchange programs.

Student loan durations may range from 5 – 15 years.

Auto Loan

Auto loans are a form of secured financing that enables you to purchase a vehicle and repay the borrowed amount over a period ranging from three to seven years.

The vehicle you buy is collateral for the loan, meaning that if you fail to make payments, the lender has the right to seize the car.

You can also use the Auto Loan Calculator for calculating payments for your auto loan.

Mortgage

Mortgages are a type of loan that is designed for purchasing real estate properties. The property being bought is offered as collateral for the loan.

Mortgages typically come with predefined terms, including the interest rate, repayment period (usually 15, 20, or 30 years), and monthly installments. The borrower makes regular monthly payments over the agreed-upon period until the loan and interest are fully repaid. For most people, this will be one of the larger amounts of money they borrowed.

How is the Periodic Payment Amount Calculated?

The periodic payment amount can be calculated by using the Reducing Balance Method.

Reducing-Balance Method

Using the reducing balance method, we can calculate periodic payments by,

PMT (Reducing Balance method)=P×r×(1+r)n(1+r)n−1\text{PMT (Reducing Balance method)} = P \times \normalsize \dfrac{r\times(1 + r)^n}{(1+r)^n - 1}

Where

P → Principal It is the amount borrowed from the bank

r → Periodic Interest Rate

This rate is the periodic interest rate, and if the period is monthly, then the rate is usually obtained by dividing the advertised Annual Rate or Nominal Rate by 12

n → Total number of periodic payments

This is the number of periods of loan tenure

What is a loan amortization schedule?

A loan amortization schedule outlines the repayment plan of a loan over its entire term. It provides a breakdown of each payment, showing how much of the payment goes toward the principal (the original amount borrowed) and how much goes toward the interest (the cost of borrowing). This schedule is useful for loans where borrowers make regular fixed payments over a set period.

Examples

Example 1

Given you procure a loan of $100,000 at 6% APY, compounded Annually and the loan tenure is for 10 years.

What is the monthly installment that needs to be made for repaying the loan within the loan tenure?

To get the monthly payment amount, you need to use the following formula

PMT (Reducing Balance method)=P×r×(1+r)n(1+r)n−1\text{PMT (Reducing Balance method)} = P \times \normalsize \dfrac{r\times(1 + r)^n}{(1+r)^n - 1}

First, you need to get the periodic interest rate, that is the monthly rate as the payback frequency is monthly. Since the interest is compounded annually, the effective interest rate for 1 year is 6% itself and the nominal interest rate per month is given by the following formula.

Nominal Yearly Interest Rate=m∗[(1+e)1m−1]=12∗[(1+6%)112−1]=5.841061%\begin{aligned}\text{Nominal Yearly Interest Rate} &= m * [(1 + e)^{\dfrac{1}{m}}- 1] \\[10pt]&= 12 * [(1 + 6\%)^{\dfrac{1}{12}} - 1] \\[10pt]&= 5.841061\%\end{aligned}
Nominal Monthly Interest Rate=5.841061%12=0.486755%\begin{aligned}\text{Nominal Monthly Interest Rate} &= \dfrac{5.841061\%}{12} \\[10pt]&= 0.486755\%\end{aligned}

The number of periods is 12M * 10Y = 120 periods. Now, the PMT is calculated as follows

PMT=$100,000∗0.4867%∗(1+00.4867%)120(1+0.4867%)120−1=$1,102.24\begin{aligned} \text{PMT} &= \$100,000 * \dfrac{0.4867\% * (1+00.4867\%)^{120}}{(1 + 0.4867\%)^{120} - 1} \\[10pt] &= \$1,102.24 \end{aligned}

The monthly payment required to pay back the loan amount is $1,102.24.

Author

hexacalculator design team

Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

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