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Difference of Compound Interest and Simple Interest
Simple interest and compound interest are two methods of calculating interest on a principal amount. The main difference between these two types of interest is that simple interest is calculated only on the principal amount, while compound interest is calculated on the principal amount plus any interest earned on that principal amount.
Simple interest is calculated by multiplying the principal amount by the interest rate and the time period. The formula for calculating simple interest is:
Simple Interest = (Principal × Interest Rate × Time)/100
For example, if you borrow $1,000 at a simple interest rate of 5% for two years, the interest you pay would be:
Simple Interest = ($1,000 × 5% × 2)/100 = $100
In contrast, compound interest is calculated by adding the interest earned on the principal amount to the principal amount, and then calculating interest on the new total. The formula for calculating compound interest is:
Compound Interest = P(1 + r/n)^(nt) – P
Where P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period.
For example, if you invest $1,000 at a compound interest rate of 5% per year, compounded annually for two years, the interest you earn would be:
Compound Interest = $1,000(1 + 0.05/1)^(1×2) – $1,000 = $105.13
As you can see, compound interest results in a higher total interest earned than simple interest, because interest is earned on both the principal amount and the interest earned in previous periods. This is why compound interest is often used for investments and savings accounts, while simple interest is used for short-term loans and other simple financial transactions.
How to find the Difference Between Simple Interest and Compound Interest?
Let us discuss in detail how to find the Difference between Simple Interest and Compound Interest. They are along the lines
Consider the Rate of Interest is the same for both Compound Interest and Simple Interest
Difference = Compound Interest for 2 years – Simple Interest for 2 Years
= P{(1+r/100)2-1} – P*r*2/100
= P*r/100*r/100
=((P*r/100)*r*1)/100
Solved Examples on Difference of Compound Interest and Simple Interest
1. Find the difference of the compound interest and simple interest on $ 10,000 at the same interest rate of 10 % per annum for 2 years?
Solution:
Simple Interest = PTR/100
= 10,000*10*2/100
= $2000
To find the Compound Interest firstly calculate the Amount
Amount A = P(1+R/100)n
A = 10,000(1+10/100)2
= 10,000(110/100)2
= 10,000(1.21)
= $12,100
Compound Interest = Amount – Principal
= 12,100 – 10,000
= $2,100
Difference between CI and SI = CI for 2 Years – SI for 2 Years
= $2100- $2000
= $100
2. What is the sum of money on which the difference between simple and compound interest in 2 years is $ 100 at the interest rate of 5% per annum?
Solution:
Simple Interest = PTR/100
Principal = P
T = 2 years
Substituting the given data in the formula for the simple interest we have
SI = (P*2*5)/100
To find the Compound Interest firstly, find out the Amount
Amount A = P(1+R/100)n
= P(1+5/100)2
CI = Amount – Principal
= P(1+5/100)2 – P
= P((1+5/100)2 -1)
Given the difference between CI and SI = $100
P((1+5/100)2 -1) – (P*2*5)/100 = $100
P((105/100)2 -1)-10P/100 = $100
P(1.1025-1)-10P/100 = $100
100P(0.1025)-10P =$10000
110.25P-10P = $10000
100.25P = $10000
P = $10000/100.25
= $99.75
Therefore, the Sum of Money is $99.75
