Compound interest calculator

What is a compound interest calculator?

A compound interest calculator is a powerful, free online financial tool used to compute the total money accumulated on your investments or savings over a specified period due to the compounding effect. Unlike simple interest, which is calculated on the principal amount alone, compound interest is calculated on the principal plus the accumulated interest from previous periods, allowing your investment to grow at a faster rate.

How does compound interest work?

Compound interest works on the principle of accruing interest on the initially invested amount, plus any interest that has previously been added. This results in an exponential increase in the total balance over time, as the interest in each compounding period is calculated on an increasingly larger amount. This principle of earning interest on interest makes compound interest especially beneficial over long periods.

Frequency of compounding interest

The frequency of compounding defines how often the accrued interest is added to the principal balance. Common compounding frequencies include annual, quarterly, monthly, and daily intervals. Frequent compounding leads to more periods for which interest is calculated, significantly increasing the final amount. For example:

• Annually: Once a year
• Quarterly: Every three months
• Monthly: Every month
• Daily: Every day, maximizing compound growth

Compound interest vs. simple interest

The primary difference between compound and simple interest lies in how each is calculated with respect to the principal. Simple interest is computed solely on the initial deposit, whereas compound interest is calculated on both the principal and the accumulated interest from previous periods. Consequently, compound interest can result in a significantly larger amount over time.

Compound interest table

Example of a compound interest table

Year	Principal	Interest Accrued	Ending Balance
1	$1,000	$50	$1,050
2	$1,050	$52.50	$1,102.50
3	$1,102.50	$55.13	$1,157.63
4	$1,157.63	$57.88	$1,215.51
5	$1,215.51	$60.78	$1,276.29

This table illustrates the effect of compounding interest annually at a rate of 5% on an initial principal of $1,000.

Formula

The standard formula for calculating compounded interest is:

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

Where:

• $A$ is the future value of the investment or savings, including interest.
• $P$ is the principal amount (initial deposit).
• $r$ is the annual nominal interest rate (decimal).
• $n$ is the number of times the interest is compounded per year.
• $t$ is the number of years the money is invested or borrowed.

Examples of use

1. For an investment of $1,000 with an annual interest rate of 5% compounded monthly for 10 years:

   • Principal $P$ = $1,000
   • Interest rate $r$ = 0.05
   • Compounding $n$ = 12 (monthly)
   • Time in years $t$ = 10

   Calculation: $A = 1000 \left(1 + \frac{0.05}{12}\right)^{12 \times 10} \approx 1,647$

2. For a deposit of $500 at an annual interest rate of 7% compounded annually for 5 years:

   • Principal $P$ = $500
   • Interest rate $r$ = 0.07
   • Compounding $n$ = 1 (annually)
   • Time in years $t$ = 5

   Calculation: $A = 500 \left(1 + \frac{0.07}{1}\right)^{5} \approx 701$

Notes

The effects of compounding interest are particularly significant over long periods, and choosing the right interest rate and compounding frequency can greatly amplify your financial growth. Always consider these factors when deciding on financial products.

FAQs

How does compounding frequency affect the final amount?

The frequency of compounding has a significant impact since more frequent compounding leads to increased growth. For example, compounding monthly at the same rate for the same period will result in a higher final balance than annual compounding.

What distinguishes compound interest from simple interest?

Compound interest is applied not only to the initial principal but also to accrued interest, which results in a much larger total sum over time compared to simple interest that only applies to the principal.

Is compound interest applicable to debts?

Yes, compound interest can also apply to debts, which can increase the total amount owed as interest is calculated on accumulated interest.