Simple vs. Compound Interest: An Overview

Interest is defined as the cost of borrowing money. It can also be the rate paid for money on deposit, as in the case of a certificate of deposit. Interest can be calculated in two ways: 澳洲幸运5官方开奖结果体彩网:simple interest or 澳洲幸运5官方开奖结果体彩网:compound interest.

• Simple interest is calculated on the principal, or original, amount of a loan.
• Compound interest is calculated on the principal amount and the accumulated interest of previous periods and can, therefore, be referred to as “interest on interest.”

There can be a big difference iღn the amount of interest payable on a loan if inter꧟est is calculated on a compound basis rather than on a simple basis. But the magic of compounding can work to your advantage when it comes to your investments. It can be a potent factor in wealth creation.

澳洲幸运5🀅官方开𒀰奖结果体彩网:Simple interest and compound interest are basic financial concepts, but becoming thoroughly familiar with them may help you make more informed decisions when you're taking out a loan or investing. 澳洲幸运5官方开奖结果体彩网:Cumulative interest can also help you choose one ☂bond inv🧸estment over another.

Simple Interest Formula

The formula for calculating simple interest is:

$\begin{aligned}&\text{Simple Interest} = P \times i \times n \\&\textbf{where:}\\&P = \text{Principal} \\&i = \text{Interest rate} \\&n = \text{Term of the loan} \\\end{aligned}$​Simple Interest=P×i×nwhere:P=Principali=Interest raten=Term of the loan​

The total amount of interest payable by the borrower is calculated as $10,000 x 0.05 x 3 = $1,500 if simple interest is charged at 5% on a $10,000 loan that's taken out for three years. Interest on this loan is payable at $500 annually or $1,500 over the three🌳-year loan term.

Compound Interest Formula

The formula for🎃 calculating the total amount paid on a loan with compound ♋interest is:

$\begin{aligned}&A=P\left(1+\frac{r}{n}\right)^{nt}\\&\textbf{where:}\\&A=\text{Final amount}\\&P=\text{Initial principal balance}\\&r=\text{Interest rate}\\&n=\text{Number of times interest applied}\\&\qquad\text{per time period}\\&t=\text{Number of time periods elapsed}\end{aligned}$​A=P(1+nr​)ntwhere:A=Final amountP=Initial principal balancer=Interest raten=Numꦦber&nbs✨p;of times interest appliedper time periodt=Number of time pe♓riods elapsed​

Compound Interest equals the total amount of principal and interest in the future, or 澳洲幸运5官方开奖结果体彩网:future value, less the principal amount at present, referred to as 澳洲幸运5官方开奖结果体彩网:present value (PV). PV is the current worth of a future sum of money or stream of cash flows ꦅgiven a specified rate of return. 

What would the amount of interest in the simple interest example be if it w♉as charged on a compound basis?

$\begin{aligned} \text{Interest} &= \$10,000 \big( (1 + 0.05) ^ 3 - 1 \big ) \\ &= \$10,000 \big ( 1.157625 - 1 \big ) \\ &= \$1,576.25 \\ \end{aligned}$Interest​=$10,000((1+0.05)3−1)=$10,000(1.157625−1)=$1,576.25​

The total interest payable over the three-year period of this loan is $1,576.25, unlike simple interest, but the interest amount isn't the same for all three years becღause compound interest 🌄also considers the accumulated interest of previous periods. Interest payable at the end of each year is shown like this:

Compounding Periods

The number of compounding periods ma🥂kes a significant difference when calculating compound interest. The higher the number of compounding periods, the greater the amount of compound interest generally is.

The 𒁃amount of interest accrued at 10% annually will be lower than the interest accrued at 5% semiannually for every $100 of a loan over a certain period. This will in turn be lower than the interest accrued at 2.5% quarterly.

The variables “i” and “n” within the parentheses have to be adjusted in the formula for calculating co🧸mpound interest if the number of compounding periods is more than once a year.

“I♕” or interest rate has to be divided by “n,” the number of compounding periods per year. “N” has to be multiplied by “t,” the total length of the investment, outside the parentheses. So i = 5% (i.e., 10% ÷ 2) and n = 20 (i.e., 10 x 2) for a 10-year loan at 10% where interest is compounded semiannually: the number of compounding periods = 2.

Yo🐓u would use thiꦛs equation to calculate the total value with compound interest:

$\begin{aligned} &\text{Total Value with Compound Interest} = \Big( P \big ( \frac {1 + i}{n} \big ) ^ {nt} \Big ) - P \\ &\text{Compound Interest} = P \Big ( \big ( \frac {1 + i}{n} \big ) ^ {nt} - 1 \Big ) \\ &\textbf{where:} \\ &P = \text{Principal} \\ &i = \text{Interest rate in percentage terms} \\ &n = \text{Number of compounding periods per year} \\ &t = \text{Total number of years for the investment or loan} \\ \end{aligned}$​🐼Total Value with Compound Interest=(P(n1+i​)nt)−PCompound Interest=P((n1+i​)nt−1)where:P=Principali=Interest rate in p♛ercentage termsn=Number&nbs🤪p;of compounding periods per yeart=Total n🍸umber of years for the&nbs💖p;investment or loan​

This table demonstrates the difference the number of compounding periods can make over time for a $10,000 🐭loan taken fo🌊r a 10-year period. 

Other Compound Interest Concepts

Compound interest doesn't only relate to loans.

Time Value of Money

Money isn't “free” but has a cost in terms of interest payable, so it follows that a dollar today is worth more than a dollar in the future. This concept is known as the 澳洲幸运5官方开奖结果体彩网:time value of money, and it forms the basis for relatively advanced techniques like 澳洲幸运5官方开奖结果体彩网:discounted cash flow (DFC) analysis.

The opposite of compounding is known as 澳洲幸运5官方开奖结果体彩网:discounting. The discount factor can be thought of as the reciprocal of the interest rate. It's the factor by which a future value must be multiplied to get the presen𒈔t value. The formulas for obtaining the📖 future value (FV) and present value (PV) are:

$\begin{aligned}&\text{FV}=PV\times\left[\frac{1+i}{n}\right]^{(n\times t)}\\&\text{PV}=FV\div\left[\frac{1+i}{n}\right]^{(n\times t)}\\&\textbf{where:}\\&i=\text{Interest rate in percentage terms}\\&n=\text{Number of compounding periods per year}\\&t=\text{Total number of years for the investment or loan}\end{aligned}$​FV=PV×[n1+i​](n×t)PV=FV÷[n1+i​](n×t)where:i=Interest rate in ♔percentage termsn=Number of com꧒pounding periods per yeart=Total number&n🌠bsp;of years for the in💎vestment or loan​

The Rule of 72

The 澳洲幸运5官方开奖结果体彩网:Rule of 72 calculates the approximate time over which an investment will double at a given rate of return or interest “i.” It's given by (72 ÷ i). It can only be used for annual compounding but it can be very helpfꦦul in planning how much money you might expect to have in retirement.

An investment that has a 6% annual rate of return will double in ♉12 years (72 ÷ 6%). An investment with an 8% annual💦 rate of return will double in nine years (72 ÷ 8%).

Compound Annual Growth Rate (CAGR)

The 澳洲幸运5官方开奖结果体彩网:compound annual growth rate (CAGR) is used for most financial applications that requ🌱ire the calculation of a single growth rate over a period.

What is the CAGR if your investment portfolio has grown from $10,000 to $16,000 over five years? PV = $10,000, FV = $16,000, and nt = 5, so the variable “i” has to be calculated. It can be shown that i = 9.86% using a financial calculator or 澳洲幸运5官方开奖结果体彩网:Excel spreadsheet.

Your initial investment (PV) of $10,000 is shown with a negative sign, according to the cash flow convention, because it represents an outflo💝w o🌼f funds. PV and FV must necessarily have opposite signs to solve “i” in the above equation.

Applications in Investing

CAGR is used extensively to 澳洲幸运5官方开奖结果体彩网:calculate returns over periods for stocks, mutual funds, and inve🐟stment portfolios. It's also u🐬sed to ascertain whether a mutual fund manager or portfolio manager has exceeded the market’s rate of return over a period.

A fund manager has 澳洲幸运5官方开奖结果体彩网:underperformed the market if a market index has provided total returns of 10% over five years, but the manager h🥃as only generated anꦓnual returns of 9% over the same period.

CAGR can also be🙈 used to calculate the expected growth rate of investment portfolios over long periods. This is useful for purposes such as saving for retireme⛎nt. Consider these examples:

1. A risk-averse investor is happy with a modest 3% annual rate of return on their portfolio. Their present $100,000 portfolio would, therefore, grow to $180,611 after 20 years. But a risk-tolerant investor who expects an annual rate of return of 6% on their portfolio would see $100,000 grow to $320,714 after 20 years.
2. CAGR can be used to estimate how much must be stowed away to save for a specific objective. A couple who would like to save $50,000 toward a down payment on a condo over 10 years would have to save $4,165 per year if they assume an annual return (CAGR) of 4% on their savings. They would have to save $3,975 annually if they’re prepared to take on additional risk and expect a CAGR of 5%.
3. CAGR can also be used to demonstrate the virtues of investing earlier rather than later in life. A 25-year-old would have to save $6,462 per year to attain their goal if the objective is to save $1 million by retirement at age 65 based on a CAGR of 6%. A 40-year-old would have to save $18,227 or almost three times that amount to attain the same goal.

Additional Considerations

Make sure you know the exact annual percentage rate (APR) on your loan because the method of calculation and number of compoundinꦺ🔜g periods can have an impact on your monthly payments.

Compounding can work in your favor when it comes to your investments but it can also work for you when you're making loan repayments. Making half your mortgage payment twice a month rather than the full payment once a month will end up cutting down your amortization period and saving you a substantial amount of interest.

Compounding🅷 can work against you, however, if you carry loans with very high rates of interest like credit card or department store debt. A♛ credit card balance of $25,000 carrying at an interest rate of 20% compounded monthly would result in a total interest charge of $5,485 over one year or $457 per month. 

How Will I Use This in Real Life?

Knowing the implications of using simple or compound interest will help you make better financial decisions.✨ If you take out a loan, knowing how the interest is calculated will allow you to choose the best loan terms and prevent you from paying too much in interest.

For example, if you take out a car loan with simple interest, it will generally cost less over time than a loan with compound interest. Conversely, when it comes to investment or savings products, you'll want compound interest because your money will grow faster.

Knowing the ins and outs of interest and how it impacts your financial decisions will help you create better financial strategies, whether that be for retirement planning, saving up to buy a house, growing your wealth, or borrowing money.

The Bottom Line

Get the magic of compounding working for you by investing regularly and increasing the frequency of your loan repayments. Familiarizing yourself with the basic concepꦬts of simple interest and compound interest will help you make better financial decisions, saving you thousands🔴 of dollars and boosting your net worth over time.