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elucidates the distinction between simple interest and compound interest, along with highlighting their significant disparities. Interest payments can be viewed as the cost of borrowing funds in the market; these are compensated by the borrower to the ler at the of a loan term. These payments typically represent a percentage of the principal amount borrowed from the ler.
Simple interest calculates total interest based on a fixed principal sum, with accrued interest not contributing to the principal over time. Let's consider :
Imagine investing $2,000 in a four-year deposit offering 12 simple interest.
Total Interest Earned: Principal Interest Rate Time = $2,000 12 4 = $960
Average Annual Interest: Total Interest Earned Time = $960 4 = $240
Amount Repd: Principal + Total Interest = $2,000 + $960 = $2,960
Compound interest operates with a variable principal sum that grows as the accrued interest is added to the original amount. It calculates total interest based on the principal and all accumulated interests over time.
For example:
Suppose you invest $2,000 in a four-year deposit paying 12 annual interest compounded annually:
Total Interest Earned: Principal 1 + Rate^Years – 1 = $2,000 1 + 12^4 – 1 ≈ $1,147.04
Average Annual Interest: Total Interest Earned Time = $1,147.04 4 ≈ $286.76
The following Excel spreadsheet vividly illustrates the considerable differences between simple interest and compound interest:
In our annual compounding example, we could adjust for semi-annual or quarterly compounding instead. We can even calculate interest on a dly basis.
Continuous compounding applies periodic recalculations of principal continuously over time. The formula to find continuously compounded interest is:
A = Pe^rt
Where:
P is the principal amount initial investment
r is the annual rate of interest
t is the number of years
e is Euler's number, approximately equal to 2.7183
For our example, if $2,000 is lent for four years at an annual interest rate of 12 compounded continuously, you would earn a total interest of $1,232.15.
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Simple Interest vs Compound Interest Comparison Understanding Basic Financial Concepts Simple Interest Calculation Methodology Compound Interest Growth Explanation Continuous Compounding in Finance Interest Rate Types Overview