Auto and Interest Loan Calculator

There is a Compound Interest Calculator One can use to find both: how much money can be accumulated via simple interest on a fixed principal amount, and how much I need to be contributing at periodic pips and how much will get at the end. Optional manifesto factors you can crunch in, like the tax on interest income and inflation.

Interest is the cost of borrowing an amount of money as a percentage or dollar amount that the borrower pays back to the lender. At the heart of (most) financial instruments in the world is the concept of interest.

There are two separate pathways to interest accumulation, called simple interest or compound interest.

Simple Interest

Here is a simple illustration of how interest functions. Introducing Morty: Derek wants to borrow $100 (the principal, as it’s often called) from the bank for a year. The bank is seeking 10% on it. To calculate interest:

$100 × 10% = $10

Interest on this is added to the principal, and this total is Derek’s amount to be paid back to the bank one year hence.

$100 + $10 = $110

A year later, Derek owes the bank $110—$100 for the principal and $10 as interest.

Now let’s say that instead of borrowing $100 for one year, Derek wanted to borrow $100 for two years. He would just be charged interest rates, right, at the end of each year, twice.

The total deduction for the long-term capital loss will be: $100 + $10(year 1) + $10(year 2) = $120

Two years later, Derek owes the bank $120—100% for the principal, plus $20 in interest.

Simple interest can be calculated as follows:

interest = principal × interest rate × term

If more complex frequencies for applying interest, like monthly or daily, are involved, then use this:

interest = principal × interest rate × definitive time period

Term

frequency

Even when people use the common word interest, they typically mean interest that compounds.

Compound Interest

As interest compounds, it needs more than one period, so let’s return to the example of Derek, who borrowed $100 from the bank for two years at a 10% interest rate. In the first year, we compute interest just as we normally would.

$100 × 10% = $10

This interest is compounded with the principal and the total is what Derek has to pay the bank at that point in time.

$100 + $10 = $110

But another end of a year and another beginning of a cycle. Interest earned on interest means that instead of the original amount, the principal + any interest that has been earned since is used. In Derek’s case:

$110 × 10% = $11

So Derek’s interest charge at the end of year 2 is $11 This is in addition to what is due after year 1:

$110 + $11 = $121

If simple interest were used instead, when the loan matures, the bank would receive either $120 or $1200, but with compounded interest, the bank collects $121 [the difference being] paid for by Derek. That’s because you also earn interest on top of it.

Where a period ends more often, higher interest will be earned on an original principal. The following shows a $1,000 investment at different compounding frequencies generating 20% interest.

In the beginning, there is very little difference between all frequencies, but they gradually begin to deviate with time. This is the wonder of compound interest everybody Robert Kiyosakied and Microsoft Excel’d about, in one small graph. Continuous compounding does have the highest return as it is based on the mathematical limit of compounding at a frequency as you approach an arbitrary time.

The Rule of 72

The rule of 72 can be very useful for anyone who needs to estimate compound interest in his or her head. Not for precise calculations as per financial calculators, but to get a sense of ballpark estimates. The rule professes that to determine the number of years (n) needed to double your money at any interest rate, just divide 72 over that same rate.

Example: If you have $1,000, how long will it take to double that at an 8% interest rate?

n = 72

8= 9

Answer is 9 years for 1,000 to become 2,000 at 8%. Be careful that this formula works on effectiveness in the values of interest between 6% and 10% but reasonably works for everything below 20%.

Interest Rate: Fixed vs. Floating

A loan or savings interest rate can be “fixed” or “floating.” Generally speaking, floating-rate loans or savings are a function of some reference rate, e.g., the U.S. Federal Reserve (Fed) funds rate or the LIBOR (London Interbank Offered Rate). Usually, the loan rate is slightly higher, while the savings rate is slightly lower than that in the reference rate. The bank keeps the difference as profit. Both the Fed rate and LIBOR are market interest rates on unsecured one-to-six-month inter-bank money (usually known as’repo’), but the Fed rate is the principal mechanism the Federal Reserve uses to manage the availability of money in the economy. LIBOR is a commercial rate based on the current interest rates of higher credit-rated banks. The interest calculator only works for fixed interest.

Contributions

The above Interest Calculator supports periodic deposits and contributions. This can be helpful for someone who tends to save a fixed amount at regular intervals. A critical note to make regarding contributions has to do with if they are made at the start or end of compounding periods. End-of-period periodic payments have one less interest total period per contribution.

Tax Rate

Interest income can be taxed in some forms, like bonds, savings, and certificates of deposit (CDs). It applies to U.S. corporate bonds nearly all of the time. Things like stocks are fully taxed; they’re taxed federally and in whole; others are partially taxed, like if you own U.S. federal treasury bonds, the interest earned would be taxed on a federal level but would usually be exempt at state and local levels. Taxes can make a really big difference in the final balance. So if at 20 years, Derek saves $100 at 6%, he will have:

$100 × (1 + 6%)20 = $320.71

This is tax-free. But if Derek has a marginal tax rate of 25%, he will end up with only $239.78 just because the tax rate of 25% is applied on every period of compounding.

Inflation Rate

Inflation is the continued rise in the prices of goods and services over time. Consequently, a given sum of money will buy progressively less in the future. The average inflation rate in the U.S. over the last century has been approximately 3%. To give some context, in the same period, the average annual return of the S&P 500 (Standard & Poor’s) index in the United States is approximately 10%. For further detail on inflation, see our inflation calculator.

For our interest calculator, leave the inflation rate at 0 for quick, generalized results. However, you can enter some figures to get numbers adjusted for inflation, which wouldn’t be accurate or real though.

Tax plus inflation means it’s tough to grow money’s real value. For instance, in the U.S., the marginal tax rate for the average middle-class person is about 25%, whereas the average inflation rate stands at 3%. In order to preserve the value of the money, 4% or more needs to be gained at a stable interest rate or investment return rate and it is difficult to achieve.