# Simple vs. Compound Interest: Definitions and Formulas (2023)

Interest is defined as the cost of borrowing money, as in the case of interest on a loan balance. Conversely, no interest may be paid on money on deposits, as with certificates of deposit. Interest can be calculated in two ways:simple interesttherenters interest.

• Simple interestis intended for itheadmaster, or the original loan amount.
• Renters interestisis calculatedon principal and accumulated interest from previous periods, and can therefore be considered "interest of interest".

There can be a big difference in how much interest must be paid on a loan if the interest is calculated on a compound basis rather than a simple basis. On the bright side, the magic of compound interest can work in your favor when it comes to your investments and can be a powerful factor in wealth creation.

Menssimple interest and compound interestare basic financial concepts, being fully familiar with them can help you make more informed decisions when taking out a loan or investing.

## Simple interest formula

The formula for calculating simple interest is:

\begin{aligned}&\text{Simple Interest} = P \time i \times n \\&\textbf{where:}\\&P = \text{Principal} \\&i = \text{Rente} \\ &n = \text{Duration of the loan} \\\end{aligned}Simple interest=Pi×I×nwhere:Pi=headmasterI=Interest raten=Term of the loan

So if simple interest is charged at 5% on a $10,000 loan taken out over three years, then the total amount of interest paid by the borrower is calculated as$10,000 x 0.05 x 3 = $1,500. Interest on this loan is paid at$500 per year or 1,500 over the three-year term of the loan. ## Compound interest formula The formula for calculating compound interest in one year is: \begin{aligned} &\text{Compound interest} = \big ( P(1 + i) ^ n \big ) - P \\ &\text{Compound interest} = P \big ( (1 + i) ^ n - 1 \big ) \\ &\textbf{where:}\\ & P= \text{Principal}\\ &i = \text{Interest in percent} \\ &n = \text{Number of compound periods in a year } \ \ \end{match}Renters interest=(Pi(1+I)n)PiRenters interest=Pi((1+I)n1)where:Pi=headmasterI=Interest terms in percentn=Number of compounding periods in a year Compound interest = the total amount of principal and interest in the future (orfuture value) minus the current capital, which is calledpresent value(PV). PV is the present value of a future sum or flow of moneythe money flowsgiven a specifiedrate of return. Continuing with the simple interest example, what would the interest amount be if charged on a compounding basis? In this case it would be: \begin{aligned} \text{Interest} &= \10.000 \big( (1 + 0,05) ^ 3 - 1 \big ) \\ &= \10.000 \big ( 1.157625 - 1 \big ) \\ &= 1.576. \\ \end{στοιχισμένος}Interesting=10 USD,000((1+0,05)31)=10 USD,000(1,1576251)=1,576,25

While the total interest paid over the three-year term of this loan is \$1,576.25, unlike simple interest, the interest amount is not the same for all three years because compound interest also takes into account accumulated interest from previous periods. The interest rates at the end of each year appear in the table below.

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