A Detailed Comparison Between Simple Interest and Compound Interest and Their Impact on Long-Term Financial Growth and Investments

 

SIMPLE VS. COMPOUND INTEREST

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: simple interest or 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 in the amount of interest payable on a loan if interest 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.

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. Cumulative interest can also help you choose one bond investment over another.

Key Takeaways

• Interest can refer to the cost of borrowing money in the form of interest charged on a loan or to the rate paid for money on deposit.
• Simple interest is only charged on the original principal amount in the case of a loan.
• Simple interest is calculated by multiplying the loan principal by the interest rate and then by the term of a loan.
• Compound interest multiplies savings or debt at an accelerated rate.
• Compound interest is interest calculated on both the initial principal and all of the previously accumulated interest.

 

SIMPLE INTEREST FORMULA

The formula for calculating simple interest is:

​Simple Interest=P×i×n

where:

P=Principal

i=Interest rate

n=Term of the loan​

 

COMPOUND INTEREST FORMULA

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

A=P(1+r/n)^nt

where:

A=Final amount

P=Initial principal balance

r=Interest raten=Number of times interest applied per time period

t=Number of time periods elapsed​

Compound Interest equals the total amount of principal and interest in the future, or future value, less the principal amount at present, referred to as present value (PV). PV is the current worth of a future sum of money or stream of cash flows given a specified rate of return. 

 

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

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 because compound interest also considers the accumulated interest of previous periods. Interest payable at the end of each year is shown like this:

Year	Opening Balance (P)	Interest at 5% (I)	Closing Balance (P+I)
1	$10,000.00	$500.00	$10,500.00
2	$10,500.00	$525.00	$11,025.00
3	$11,025.00	$551.25	$11,576.25
Total Interest		$1,576.25

COMPOUNDING PERIODS

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

The amount 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 compound 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.

 

You would use this equation to calculate the total value with compound interest:

Total Value with Compound Interest=(P((1+i)/n))^nt)−P

Compound Interest=(P((1+i)/n))^nt)−P

where:

P=Principal

i=Interest rate in percentage terms

n=Number of compounding periods per year

t=Total number of years for the investment or loan​

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

Compounding Frequency	No. of Compounding Periods	Values for i/n and nt	Total Interest
Annually	1	i/n = 10%, nt = 10	$15,937.42
Semiannually	2	i/n = 5%, nt = 20	$16,532.98
Quarterly	4	i/n = 2.5%, nt = 40	$16,850.64
Monthly	12	i/n = 0.833%, nt = 120	$17,059.68

 

COMPOUND ANNUAL GROWTH RATE (CAGR)

The compound annual growth rate (CAGR) is used for most financial applications that require 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 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 outflow of funds. PV and FV must necessarily have opposite signs to solve “i” in the above equation.

 

WHICH IS BETTER, SIMPLE OR COMPOUND INTEREST?

It depends on whether you're investing or borrowing. Compound interest causes the principal to grow exponentially because interest is calculated on the accumulated interest over time as well as on your original principal. 

It will make your money grow faster in the case of invested assets. Compound interest can create a snowball effect on a loan, however, and exponentially increase your debt. You'll pay less over time with simple interest if you have a loan.

 

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