# Interest Calculator

Calculate the future value and interest earned for an investment or loan using simple interest or compound interest.

$% years$
$per year % years$
$## Future Value using Simple Interest:  Total Value:$6,312.50 Total Interest: $1,312.50 ### Balance by Year This calculation is based on widely-accepted formulas for educational purposes only - this is not a recommendation for how to handle your finances, and it is not an offer to lend or invest. Consult with a financial professional before making financial decisions. Learn how we calculated this below ## On this page: ## How to Calculate Interest Interest is the form of payment that a borrower pays to a lender in order to use the lender’s money. The direct lender can be a bank, but depositors at the bank are lending their money indirectly. Anyone who owns a checking or savings account at a bank is in effect lending their money to others, and part of the return that individuals seek when lending (either directly or indirectly) is the interest payment. At its most basic level, individuals can invest in two forms: by owning (stocks) or by lending (bonds). Part of the return that individuals seek when lending is the interest payment. Think about a form of debt you may have, whether it be a mortgage, auto loan, or credit card. A portion of your monthly payment each month first goes to interest and then the remaining part of the payment goes to pay off the balance. At the beginning of the loan period, a higher portion of the payment goes to interest than at the end of the loan. This is because, in the beginning, the loan amount is the largest, so the interest will also be the largest. But as you continue to pay off the loan, the principal balance becomes smaller and in relation, the interest accrued will be less. ### Simple Interest With simple interest, the interest is only paid on the principal value and never on any accrued interest. The interest that is paid (or earned) with simple interest will be less than the interest paid (or earned) with the compound interest method. You can use a simple interest calculator or a formula to calculate simple interest. The simple interest formula is as follows: A = P \times (1 + (r \times t)) where: PV = present value r = interest rate t = number of periods For example, let’s say you are going to take out a$20,000 auto loan at 4% simple interest for 5 years. How much in total interest will you pay?

A = \$20,000 \times (1 + (0.04 \times 5)) A = \$20,000 \times (1 + 0.2)
A = \$20,000 \times 1.2 A = \$24,000

So you will pay a total of $24,000 over this period. The excess above the principal value is the interest. Therefore, the total interest in this scenario will be$4,000.

### Compound Interest

With compound interest, interest is accrued on prior interest payments and the principal balance. This is the key difference between compound interest and simple interest.

Like before, you can use a compound interest calculator or a formula to calculate compound interest. The compound interest rate formula is as follows:

A = P \times \left (1 + \frac{r}{n} \right )^{nt}

where:
A = future value
PV = present value
r = interest rate
n = number of times interest is compounded per period
t = number of periods

We can use the same numbers in our prior example to see how much more interest will be paid using compound interest. We will assume here that interest is compounded annually, so n is equal to 1.

A = \$20,000 \times \left (1 + \frac{0.04}{1} \right )^{1 \times 5} A = \$20,000 \times 1.04^{5}
A = \$20,000 \times 1.2166529 A = \$24,333

The total interest in this example is $4,333 and is higher by$333 compared to the simple interest method.

Interest can be compounded at any time frequency, but the most common are continuously, daily, monthly, quarterly, semiannually, and annually. The interest calculator above gives the results for all these options.

The more frequent the compounding, the higher the total interest will be. Daily compounding will result in higher interest than annual compounding.

Let’s use the compound interest formula above to see how much higher. (we also have a daily compound interest calculator for this). Since interest is compounded daily, n will equal 365.

A = \$20,000 \times \left (1 + \frac{0.04}{365} \right )^{365 \times 5} A = \$20,000 \times 1.0109589\%^{1,825}
A = \$20,000 \times 1.22138937 A = \$24,428

The total interest in this example is $4,428. Using these assumptions, interest compounded daily is$95 more than interest compounded annually.

#### The Rule of 72

The Rule of 72 provides an easy way to approximate the amount of time needed to double an investment. This is found by dividing 72 by the interest rate you expect to earn.

If you find an investment that pays 5% a year indefinitely, the Rule of 72 states that it should take approximately 14.4 (72/5) years to double the investment. The actual number is 14.207.

The Rule of 72 calculator shows the approximation as well as the actual number.

## How to Calculate an Interest Rate

Using the assumptions in the prior examples, we can also solve what the simple interest rate will be if we are only given the interest paid instead of the rate. This formula is:

r = \frac{i}{pn}

Where:
r = interest rate
i = total interest paid
p = loan principal
n = loan term in years

Let’s back into the answer that we already found above to illustrate this calculation. If you were going to pay $4,000 in interest on a$20,000 auto loan for 5 years, what would your simple interest rate be?

r = \frac{\$4,000}{\$20,000 \times 5}
r = \frac{\$4,000}{\$100,000}
r = 4\%

We get the exact interest rate we were expecting.

The interest rate calculator gives the results for interest rate if you know the monthly payment as opposed to the total interest over the life of the loan.

There are options to select either simple or compound interest and whether the loan term is in months or years.

### APY Interest Rate

The annual percentage yield (or APY) interest rate is just another name for compounding interest. It is the real rate of return of an investment earned per year accounting for compounded interest.

In our APY calculator, enter the same assumptions from the example we have been using to see if the results are the same.

### APR Interest Rate

APR stands for annual percentage rate. The APR interest rate is closer to the simple interest rate with one twist. It includes other fees that the bank may charge you. It represents a true cost of borrowing for the individual.

If you are taking out a loan with a relatively high interest rate but low fees, you may end up with a lower APR than a loan with a low interest rate but high fees. This is why it is recommended to compare the APR between two financial institutions as opposed to comparing only the interest rates.

### Nominal Interest Rate

The nominal interest rate is found when simple interest is used. Compounding never occurs here. If the effective annual interest rate is known, then the nominal interest rate can be found.

The formula for the nominal interest rate is

i = n \times \left [ \left (1 + r \right )^{1/n} – 1 \right ]

Where:
i = nominal interest rate
r = effective annual interest rate
n = number of times per period interest is compounded

Let’s put numbers to this to get a better understanding. What is the nominal interest rate for a 3% effective annual rate compounded monthly (n = 12)?

i = 12 \times \left [ \left (1 + 0.03 \right )^{1/12} – 1 \right ]
i = 12 \times \left [ \left (1.03 \right )^{0.08333} – 1 \right ]
i = 12 \times 0.246627\%
i = 2.96\%

Note that the nominal interest rate is smaller than the effective annual interest rate that we will calculate in the following example. This is due to no compounding on the nominal interest rate. Because of no compounding, you earn less on your investment and therefore will yield a lower interest rate.

### Effective Annual Interest Rate

The effective annual rate (EAR) is the real cost of borrowing money. It differs from the nominal interest rate in that this is the compounded interest rate. With compounding, the more frequent the compounding, the more interest is paid. Let’s look at a few examples to see this.

The formula is:

EAR = \left ( 1 + \frac{r}{n} \right )^{n} − 1

Where:
EAR = effective annual rate
r = nominal interest rate
n = number of times per period interest is compounded

Let’s say you have an opportunity to lend at 3% annual interest (nominal interest rate). What is the EAR of compounding quarterly and compounding semiannually? Would you prefer compounding quarterly (n = 4) or semiannually (n = 2)?

We can insert these figures into our formula.

#### Quarterly

EAR = \left ( 1 + \frac{0.03}{4} \right )^{4} − 1
EAR = 1.00075^{4} − 1
EAR = 1.030339 − 1
EAR = 3.0339\%

#### Semiannually

EAR = \left ( 1 + \frac{0.03}{2} \right )^{2} − 1
EAR = 1.015^{2} − 1
EAR = 1.030225 − 1
EAR = 3.0225\%

Since in this example you are a lender, you would want interest compounded quarterly because that will give you a higher EAR and therefore more interest.

If the roles were reversed and you were borrowing money, then you would prefer interest to be compounded semiannually.

Here again, we see that the nominal interest rate is less than both effective annual interest rates. The simple interest rate is only applied to the original principal value, but the compounded interest rate is applied to prior interest payments and the principal amount, so you would earn interest on interest.

You can also find these results using our EAR calculator.