Difference Between Simple Interest and Compound Interest
The difference between simple and compound interest is, simple interest is calculated on principal amount whereas compound interest is calculated on the principal amount and the interest compounded for a cycle of the period. Loans such as installments loans, educational loans, use simple interest. Compound interest is used while investing as it lets funds grow at a faster rate. Compound Interest pays more interest than simple interest.
Difference Between Simple and Compound Interest
Simple interest (S.I.) is the sum paid back for using the borrowed money, over a fixed period of time whereas compound interest (C.I.)is calculated when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. The return amount of simple interest is much lesser as compared to compound interest. On the other hand, the return is much higher in compound interest.
The difference between the formulas of simple interest and compound interest is:
Here, P = Principal , R = rate of interest ,T = time duration in years, S.I. = Simple Interest and C.I. = Compound Interest
 S.I. = S.I. = (P × R × T) ⁄ 100
 C.I.= P(1+R/100)^{t} − P
Let us understand the differences in the calculations of Simple interest and compound interest when the principal is $100 for 3 years with 5 % interest. When the calculation is done with simple interest, the principal remains the same for a particular period of time. When the calculation is done with compound interest the principal is revised. The principal along with the interest accumulated in the first period is calculated as the revised principal. Thus the principal keeps on increasing with compound interest.
Simple Interest  Compound Interest 

At the end of the first year, the SI is $5  At the end of the first year, the CI is $5 
At the end of the second year, the principal taken for calculation is the same $100. SI is $10 
At the end of the first year, the principal is $100+ the interest $5= $105 and CI is $10.25 
At the end of the second year, the principal taken for calculation is the same $100. SI is $15  At the end of the second year, the principal taken for calculation is $105 + $10.25 = $115.25 and the CI is $15.76 
Using the formula, we calculate the same as SI = (PRT)/100 = (100 × 5 × 3)/100 = $15 
Using the formula, we calculate the same as: CI = P(1+R/100)^{t} − P = 100(1 + 5/100)^{3 } 100 = 100[105/100]^{3 } 100 = 1157625/ 10000  100 =$15.76 
Simple Interest vs Compound Interest
Look at the image given below which shows the differences between simple and compound interest.
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Simple Interest and Compound Interest Examples

Example 1: Find the difference between the simple interest and the compound interest on $5000 for 2 years at 9% per annum.
Solution:
S.I. = (P × R × T ) ⁄ 100 and C.I.= P(1+R/100)^{t }− P
Principal = $5000 , Time(t) = 2 years , Rate of interest (r) = 9%
S.I. = $(5000 × 9 × 2) / 100 = $900
C.I.= P(1+R/100)^{t} − P = $[5000 (1 + 9 /100)^{2}  5000]
C.I. = $[5940.5  5000] = $940.5
Difference = C.I. S.I. = $940.5  $900 = $40.5 
Example 2: Find the simple interest and the compound interest on $2500 for 2 years at 10% per annum.
Solution:
S.I. = (P × R × T) ⁄ 100 and C.I.= P(1+R/100)^{t} − P
Principal = $2500 , Time(t) = 2 years , Rate of interest (r) = 10%
S.I. = $(2500 × 10 × 2) / 100 = $500
C.I.= P(1+R/100)^{t} − P = $[2500 (1 + 10/100)^{2}  2500]
C.I. = $[3025  2500] = $525 
Example 3: Rachel borrows $20000 per annum for 2 years at simple interest and Phoebe borrows the same amount for the same time period at 12% per annum, compounded annually. Who pays more interest and by how much?
Solution:
Principal (P) = $20000, Time (T) = 3 years, Rate of interest (R) = 12% p.a.
Simple Interest for Rachel = (P × R × T) / 100 = $(20000 × 12 × 2)/100 = 200 × 12 × 2 = $ 4800
Compound Interest for Phoebe.= P(1+R/100)^{t} − P = $[20000 (1 + 12/100)^{2}  20000] = $5088
Difference = C.I. S.I. = $5088  $4800 = $288
Phoebe pays more interest by $288.
FAQs on Difference Between Simple Interest and Compound Interest
What is the Difference between Simple and Compound Interest?
Simple interest is computed on the principal amount whereas compound interest is computed based on the principal amount as well as the interest accumulated for a certain period.
What is the difference between Simple Interest and the Compound Interest on $2000 for 2 Years at 10% Perannum?
S.I. = (P × R × T) ⁄ 100 and C.I.= P(1+R/100)^{t} − P
S.I. = $(2000 × 10 × 2) /100 = $400
C.I. =$[2000 (1 + 10/100)^{2} 2000] = $420
Difference = C.I. S.I = $420  $400 = $20
The difference between the simple interest and the compound interest on $2000 for 1 year at 10% per annum is $20.
What is the Difference between Simple Interest and Compound Interest in the case of the principal amount?
The principal amount is constant in simple interest whereas, the principal amount keeps on changing during the entire borrowing period as the interest is added to the principal whenever the interest is up for the payment in compound interest.
What is the Formula of Simple Interest and Compound Interest?
The formula for simple interest is S.I. = (P × R × T) ⁄ 100, where S.I. = Simple Interest, P = Principal, R = Rate of interest, and T = Time Duration in years
The formula for compound interest is given by: C.I.= P(1+R/100)^{t} − P, where C.I. = Compound Interest, P = Principal , R = Rate of interest, and T = Time Duration in years
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