Difference Between Simple Interest and Compound Interest (2024)

Simple Interest Formula

The simple interest formula can be calculated using:

\(S.I.=\frac{\left(P\times R\times T\right)}{100}\)

Here,

“P” is the principal amount or the initial amount invested or borrowed from the bank.

“R” is the rate of interest at which the principal amount is shared with an individual for a certain time.

“T” is the time duration for which the principal amount is given to an individual.

Compound Interest Formula

The compound interest formula can be calculated using:

CI = A – P

Where A is the amount and is calculated by the formula:

\(A=P\left(1+\frac{R}{100}\right)^T\)

Hence, the final C.I. formula is:

\(C.I.=P\left(1+\frac{R}{100}\right)^T-P\)

For the above two formulas:

‘A’ stands for the amount.

‘P’ is the principal.

‘R’ denotes the rate of interest.

‘T’ is the time in years

What is an interest rate?

Interest rate is the additional amount that the individual pays whenever they borrow some money from a bank or any other source at the time of return. The interest charged can be either simple interest or compound interest.

Some Important Formulas for difference between Simple Interest and Compound Interest

The difference between compound and simple interest for two years can be determined using the below formula:

\(\text{Difference}=\frac{P\left(R\right)^2}{\left(100\right)^2}\)

This can also be written as, \(\text{Difference}=P\times\frac{R}{100}\times\frac{R}{100}\)

The difference between compound and simple interest for three years can be determined using the below formula:

\(\text{Difference}=3\times\frac{P\left(R\right)^2}{\left(100\right)^2}+P\left(\frac{R}{100}\right)^3\)

This can also be written as:

\(\text{Difference}=P\left(\frac{R}{100}\right)^2\left(\frac{R}{100}+3\right)\)

For both formulas; P is the principal amount and R is the rate of interest.

Difference Between Simple Interest and Compound Interest Solved Examples

The idea of S.I. is the amount spent for the capital borrowed for a specified time. On the other hand in compound interest, the interest every time is added back to the principal amount.

Let us step toward some solved examples to understand simple interest vs compound interest.

Solved Example 1: What is the difference between simple interest and compound interest for two years if the principal amount is Rs 1000 and the rate of interest is 10%?

Solution:

Given data:

T = 2 years

P = Rs. 1000

R = 10%

Method 1:

\(C.I.=P\left(1+\frac{R}{100}\right)^T-P\)

⇒ \(1000\left(1+\frac{10}{100}\right)^2-1000\)

⇒ Rs. 210

\(S.I.=\frac{\left(P\times R\times T\right)}{100}\)

⇒ \(\frac{1000\times10\times2}{100}\)

⇒ Rs. 200

Difference = CI – SI = 210 – 200

Difference = Rs 10.

∴ The difference between compound interest and simple interest CI and SI for 2 years is Rs. 10.

Method 2:

The difference between simple and compound interest can also be calculator directly by the formula:

\(\text{Difference}=P\times\frac{R}{100}\times\frac{R}{100}\)

\(=1000\times\frac{10}{100}\times\frac{10}{100}\)

The difference between compound interest and simple interest for 2 years=10

Solved Example 2: If the difference between S.I. and C.I. at a 10% per annum rate of interest for 3 years is Rs. 930, then find the principal value.

Solution:

Given:

Rate of interest = 10%

Time = 3 years

Difference between compound interest and simple interest for 3 years = Rs. 930

The formula used is:

\(\text{Difference}=P\left(\frac{R}{100}\right)^2\left(\frac{R}{100}+3\right)\)

\(930=P\left(\frac{10}{100}\right)^2\left(\frac{10}{100}+3\right)\)

\(P=930\times\left(\frac{100}{10}\right)^2\times\left(\frac{100}{310}\right)\)

After solving we get:

P =30,000

Solved Example 3: The difference between compound interest and simple interest for 3 years is Rs. 616 at 8% per annum. Obtain the value of the compound interest in 2 years at the same rate of interest at the same sum.

Solution:

Given that for 3 years, the difference between simple interest and compound interest = Rs. 616

Rate = 8%

Therefore P can be obtained through the formula:

\(\text{Difference}=P\left(\frac{R}{100}\right)^2\left(\frac{R}{100}+3\right)\)

⇒\(616=P\left(\frac{8}{100}\right)^2\left(\frac{8}{100}+3\right)\)

⇒\(616=P\left(\frac{64}{10000}\right)\left(\frac{308}{100}\right)\)

⇒\(P=\frac{\left(616\times10000\times100\right)}{\left(308\times64\right)}\)

⇒ Rs. 31,250

Now:

\(C.I.=P\left(1+\frac{R}{100}\right)^T-P\)

⇒\(31250\left\{\left(1+\frac{8}{100}\right)^2-1\right\}\)

⇒\(31250\times\left\{\left(\frac{108}{100}\right)\times\left(\frac{108}{100}\right)-1\right\}\)

⇒\(31250\times\left\{\left(\frac{11664}{10000}\right)-1\right\}\)

⇒ Rs. 5200

∴ The C.I. in two years at the same rate of interest at the same sum is Rs. 5200.

Solved Example 4:The difference between simple interest for one year and compound interest for the half year on Rs. 1200 at 10% per annum is?

Solution:

\(S.I.=\frac{\left(P\times R\times T\right)}{100}\)

\(S.I.=\frac{\left(1200\times10\times1\right)}{100}\)

P = Rs. 120

For calculating the compound interest,

Principal = Rs. 1200

Time period = two years

Rate = 10/2 = 5%

\(C.I.=P\left(1+\frac{R}{100}\right)^T-P\)

=\(C.I.=1200\left(1+\frac{5}{100}\right)^2-1200\)

= Rs. 123

Therefore the difference = CI – SI = 123 – 120 = Rs. 3

∴ The difference between simple interest for one year and compound interest for the half year on Rs. 1200 at 10% per annum is Rs. 3

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