I would like to calculate..
interest rate on loan
Specifications
Loan amount
$
Term
yrs
mos
Interest capitalization frequency
monthly
Periodic payment
$
Payment frequency
monthly
Prepaid fees
$
Loaned fees
$
Results
The annual nominal interest rate is 13.1167% with a periodic rate of 1.1612%.
The effective annual rate (EAR) is 13.9347%.
The Annual Percentage Rate (APR) is 14.9759%.
The total payments amount to $18,500, with an interest of $8,000 and additional fees of $500.
The periodic payment, after rolling the additional fee into the loan, becomes $159.52.
Percentage breakdown
Annual balances
Display results in
chart

This interest rate calculator is a compact tool that allows you to estimate various types of interest rate on either a loan or deposit account. You may find yourself in a situation where you take a loan and you know only the due payments, or you keep money in a bank and you know only your initial deposit and the current balance. In such circumstances, this calculator can help you find out the interest rate.

You can use this device, for example, as an effective interest rate calculator, car loan interest rate calculator, or saving interest rate calculator. One of the main strengths of this tool is the comprehensive specification. For example, you can set any additional fees that mostly arise in mortgage loans. Therefore, by considering such extra costs, you can use the tool as an Annual Percentage Rate (APR) calculator and compare different offers. Besides, you can set the frequency of the interest capitalization or compounding frequency continuous as well.

In the following, you can learn what is the interest rate in different contexts and read about how to calculate the interest rate on a loan. You can also study the results through visual representations. You can check, for example, the proportion of interest in the Percentage breakdown, or follow the progress of your Annual balances in a chart or table.

If you are more interested in investments you can find the interest rate and other factors with our investment calculator, or you may have a look at the IRR calculator, which can help you to estimate the profitability of potential investments.

What is interest rate?

In general, when someone borrows from or make a deposit at a bank, the amount to be paid back or received is higher than the original amount, called the principal. The difference between the two amounts embodies the interest. The interest rate, therefore, represents the proportion of this interest amount to the original loan or deposit, usually expressed as a yearly percentage. More formally, it is the rate a financial institution charges for borrowing its money or the rate a bank pays its depositors for holding money in an account.

An important concept is compounding interest, which means that interest incurred over a specific interval is added to the principal amount. In other words, the base of the interest calculation (the principal) includes the previous period's interest; thus, the total amount grows exponentially. If you are interested, you may check our compound interest calculator, where you can study the real power of compounding in different scenarios on a dynamic chart.

A short survey on bank interest rates

Since interest rate can take numerous forms, getting familiar with their distinctive features not only helps you distinguish between them, but also gives you a handy guide in the financial world. Besides, as you can estimate the most prevailing interest rates with this interest rate calculator, it is essential to know what their effect is on your personal finance.

The calculator has been designed to estimate bank interest rates on a loan or deposit, so we focus on the following most frequently used rates in such financial transactions:

  • Nominal Annual Interest Rate r
  • Periodic Rate i
  • Effective Annual Rate EAR
  • Annual Percentage Rate APR
  1. Nominal Annual Interest Rate

The most common interest rate is a nominal annual interest rate, also known as simple interest (or headline or quoted interest rate). If you hear someone talking about a rate in a conversation related to finance, the person likely refers to a nominal interest rate. It is also the figure that banks often advertise as the interest rate on a financial transaction. From the borrower's perspective, it represents the borrowing cost of the loan for a year, represented as a percentage of the loan amount. From the perspective of the lender or investor (depositor), it defines the interest earned on the transaction over a year. While the nominal interest rate provides a simple option to measure the yearly cost of the loan or earnings on a transaction, two important factors mean that we should often consider other interest rates:

  • nominal interest rate doesn't account for the effect of compound interests.
  • it also doesn't cover any additional cost beyond the interest, which is especially relevant at mortgage loans.
  1. Periodic Rate

Before we talk about other rates adjusted by the above factors, it is practical to talk about an interest rate applied over a specific period. Since compounding or interest capitalization generally occurs more often than once a year, it is useful to know the rate that is charged on a loan, or realized on a saving/investment over a specific period covering a compounding interval. This rate is the periodic rate.

The simple way to get the periodic interest rate is the following:

periodic rate = nominal interest rate / number of compounding.

  1. Effective Annual Interest Rate (EAR)

Going back to the previously mentioned shortages of the nominal interest rate, if we take into account the effect of compounding interest, we obtain the Effective Annual Rate (EAR or EFF%). The concept of EAR is the same as that for the Annual Percentage Yield (APY), however, the latter form is applied mainly on investments or savings account. Since the compounding period may vary in different types of financial instruments, one of the main advantages of the Effective Annual Rate is that the financial products became comparable. For example, while a deposit account (A) with a 10.1 percent nominal interest rate compounded semi-annually may seem to be a better option than a savings account (B) that offers 10 percent compounded monthly, by computing their APY we can perform a precise comparison.

By the following financial formula you can compute the APY or EAR:

EAR = ((1 + periodic rate)number of compounding - 1) * 100

periodic rate (A) = 10.1 / 2 = 5.05% = 0.0505

periodic rate (B) = 10 / 12 = 0.83% = 0.0083

APY (A) = ((1 + 0.0505)2 - 1) * 100 = 0.1036 = 10.36%

APY (B) = ((1 + 0.0083)12 - 1) * 100 = 0.1047 = 10.47%

As you can see, the APY for option B with a lower nominal interest rate is around 0.11 percentage point higher than for the option A offering higher nominal rate. While the difference seems to be minor, if the underlying values are high and the transaction is considered over a considerable interval, the difference in interest earnings might become ample.

  1. Annual Percentage Rate (APR) - APR vs interest rate

Stepping forward, you may find yourself in a situation where the second point is relevant: there are additional costs connected to the loan besides interest that increase your final expense. Since banks are profit-oriented, they aim to maximise their financial gain by obtaining low-cost funds (deposits) and lending out money as expensively as possible (loans). Highly simplifying their operation, the difference between the two transactions is their profit. To acquire more income, however, they might provide other services that they additionally charge to the borrower.

APR is aimed at imparting and pointing out these fees and expressing them in the yearly rate. Therefore, APR might be a better measure when you are about to evaluate the real cost of borrowing or want to compare different loan offers.

If you would like to get more details on this topic, you may like to visit our APR calculator. It not only provides a comprehensive description, but also allow you to compute the Effective APR that incorporates the compounding effect as well.

Note that the altering the buying power of the money also affects the real value of the interest you pay or receive, especially over a long period. When you adjust the nominal rate by inflation, you get to the concept of the real interest rate, which is an important measure in economics.

To conclude, the table below sums up the main peculiarities of the interest rates mentioned above:

Considerations Nominal Interest Rate (r) Effective Annual Rate (EAR) Annual Percentage Rate (APR)
Alternative terms Headline, Quoted interest APY, EFF% n/a
Effect of compounding No Yes No
Inclusion of additional costs No No Yes
Application Broad Broad Loans

Using the interest rate calculator - how to calculate interest rate?

Now that you have gained some knowledge on different type of interest rates, to be able to use this tool, it is essential to get familiar with the specification of our interest rate calculator so that you can analyse a loan or a deposit from different angles.

As a starting point, you need to choose what the subject is of your interest: a loan or a deposit.

After this selection, you can compute the previously mentioned interest rates by specifying the following parameters:

  1. Specification
  • Loan amount (A) - the amount of loan under consideration. This is also the principal.

  • Term (t) - the interval over which you need to repay the loan amount and all connected cost (interest and other additional fees).

  • Interest capitalization frequency (m) - the number of times interest compounding occurs in one year. For example, when compounding is applied annually, m=1, when quarterly, m=4, monthly, m=12, etc. You can choose the frequency as continuous as well, which is an extreme form and the theoretical limit of compounding frequency. In such a case, the number of periods when compounding occurs is infinite thus compounding happens in every possible moment. To see its mathematical background, you may check the section called Natural logarithm in the log calculator.

  • Payment frequency (q) - the regularity with which part of the loan is repaid.

  • Periodic payment (P) - the amount of money to be paid in each period defined by the payment frequency.

  • Prepaid fees - fees that are payable in advance (Prepaid Finance Charge) or at the time the loan is consummated. Interest is not charged on these fees, but it still affects the APR of a loan.

  • Loaned fees - all additional fees that are rolled into the loan. Since it is attached to the loan amount, banks generally charge interest on it.

  • Current balance - the amount of money held in the deposit account.

  • Initial Deposit - the opening balance of the account.

  1. Results

After you set all required field you will immediately get the related interest rates.

  • Annual Nominal Interest Rate and the Periodic Rate - unadjusted rates for a year and for a compounding period.

  • Effective Annual Rate (EAR) - an estimate of the yearly rate adjusted by the compounding effect. As mentioned above, this indicator doesn't account for any additional costs attached to the loan.

  • Annual Percentage Rate (APR) - estimates the cost of borrowing per year as a percentage of the Loan Amount. It takes into consideration all additional costs without incorporating the compounding factor.

  1. Percentage breakdown

The figure in this section shows you how the total payments (loan) or total balance (deposit) built up, broken down into the following components:

  • Loan amount or Initial deposit - the part of the principal in the financial transaction.

  • Total interest - the sum of the interest paid (loan) or earned (deposit).

  • Total additional fees - the sum of all costs connected to the loan (fees rolled into the loan plus fees paid separately).

  1. Annual Balances

In this section you can study in detail the progress of your balances on a chart or in a table.

How to calculate interest rate on a loan or on a deposit?

Computing interest rates, particularly ones with sophisticated specifications, involves a series of equations where the interest rate is the base of an exponentiation. One efficient way to deal with such an equation is to apply the so-called Newton-Raphson method, which is a mathematical algorithm using an iteration procedure.

The applied computations involves the concept of time value of money, and can be reduced to the following two formulas:

Regarding the loan interest rate:

P = (A * i * (1 + r / m)mt) / ((1 + r / m)mt - 1),

where:

  • P stands for the periodic payment
  • A is the loan amount (or principal)
  • i is the periodic rate
  • r represents the interest rate
  • t is the number of years
  • m is the frequency of compounding or interest capitalization

Regarding the deposit (savings) interest rate:

F = A * (1 + r / m)mt,

where:

  • F stands for the current balance (future value)
  • A is the initial deposit

Disclaimer

The results of this calculator, due to rounding, should be considered as just a close approximation financially. For this reason, and also because of possible shortcomings, the calculator is created for advisory purposes only.

Tibor Pal, PhD candidate