# Compound Interest Calculator

Project your potential long-term investment returns. See the impact of compounding frequency, additional contributions, years to grow, and different interest rates.

Future Balance

\$16,722

If you’re looking for a long-term investment strategy, we’ve got you covered. Titan’s award-winning, expert-managed portfolios offer investors of all income levels the potential to grow their wealth over the long-term.

## How Titan’s compound interest calculator works

Titan’s compound interest calculator gives anyone the ability to see how compounding interest could affect investment returns over a period of time. This calculator also shows the potential growth from making regular additional investments through strategies such as dollar-cost averaging.

Here is how the compound interest calculator works based on the following inputs:

Initial deposit: This is the amount of money you might initially invest.

Additional contributions: This is how much you might add on a consistent basis beyond the initial deposit.

Contribution frequency: This reflects how often you might add money, whether monthly or annually.

Investment length: This is how long the investment is held. The longer the timespan, the greater the potential benefit of compound interest and growth. The future balance feature of Titan’s compound interest calculator shows the effect of increasing the investment length, with an upward sloping curve indicating estimated future wealth.

Interest rate: Titan's compound interest calculator uses a 5% default interest rate, but you can adjust this to match the interest rate on a savings or investment account.

Compounding frequency: Some savings accounts and money market accounts compound interest daily, while others are compounded monthly. Investment and brokerage accounts generally compound quarterly or semi-annually. More frequent compounding results in faster wealth growth.

If you use multiple online calculators and compare the results, you might notice that Titan’s calculator yields different results than others. That’s because Titan’s calculator assumes that, for purposes of compounding, each month is 30.4 days, by dividing 365 days into 12 months. Other calculators sometimes use an exact number of days for each calendar month.

## What is compound interest?

Interest is either the amount paid to borrow money, or the amount received for lending money. It’s expressed as a percentage of the amount borrowed or lent, called the interest rate, for the period of time the money is borrowed or lent. The most common period for calculating interest rates is annual. For example, \$100 borrowed or lent for one year at a 5% annual rate would produce \$5 of interest; the borrower pays \$5 in addition to repaying \$100, and the lender receives \$5 plus \$100.

Compound interest is the calculation of interest on the original principal plus the accumulated interest from the first and subsequent periods. It’s interest on interest, in addition to interest earned on the original principal.

Here’s an example of how compound interest works across several years:

Imagine an initial investment of \$25,000, which will earn an annual interest rate of 5%. This investment is held for three years, and the interest received is reinvested each year. The interest rate is expressed in decimal form.

 Time Year 1 Year 2 Year 3 Principal \$25,000.00 \$26,250.00 \$27,562.50 Rate 5% 5% 5% Interest \$1,250.00 \$1,312.50 \$1,378.13 Balance \$26,250.00 \$27,562.50 \$28,940.63

So after three years, the initial investment has grown to \$28,940.63.

## What is the formula for compound interest and how does it work?

The compound interest formula is as follows:

A = P(1 + r / n)nt

Where (A) total principal and compound interest equals:

1. The original principal, P.

2. Multiplied by 1 plus the annual interest rate (r) divided by the number of times (n) interest is paid each year.

3. Increased by the power of the number of interest payments each year times the number of years of compounding (nt).

The last part of the formula is the key to compounding interest: the nt term is an exponent of the interest rate, not just a multiple. From basic math, values increase faster by exponentiation than multiplication.

Using the example above, the formula would look like this based on \$25,000 invested for three years at an annual 5% interest rate:

\$28,940.63 = \$25,000 X (1.05 to the third power, or 1.05 cubed)

Compounding each year resulted in \$3,940.63 in accumulated interest on the original \$25,000. Without compounding, the accumulated interest would be \$1,250 times three years, or \$3,750. That’s \$190.63 less than what compounding produces.

## What is the difference between simple interest and compound interest?

Interest that isn’t compounded is called simple interest. It is the rate of interest computed on the original principal alone, not on the additional interest. If done over a number of years, simple interest is merely the dollar amount of interest earned from the first year, multiplied by the number of years for the assumed investment, also known as the horizon.

Here is how the advantage of accumulated wealth from compound interest widens over simple interest, using the \$25,000 example above, in five-year intervals:

 Years Compound Simple Difference 5 \$31,907.00 \$31,250.00 +\$657.00 10 \$40,722.00 \$37,500.00 +\$3,222.00 15 \$51,973.00 \$43,750.00 +\$8,233.00 20 \$66,332.00 \$50,000.00 +\$16,332.00 25 \$84,658.00 \$56,250.00 +\$28,408.00

The table shows that sometime between 10 and 15 years, the compound interest earned exceeded the original \$25,000 investment, also known as the principal. By the end of year 15, compound interest totaled \$26,973 (\$51,973 - \$25,000).

This shows how the dynamic of compound interest or compound returns works—each additional year of savings or investment makes the advantage of compounding larger compared to simple interest.

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