Simple interest and compound interest are concepts that are very useful in real life for calculating the interest over the amount borrowed or lent out, for a certain period of time at a certain rate of interest. Now, let’s individually explore each type of these interests.

Compound Interest and Simple Interest formula

Simple Interest

Simple interest is the interest that is calculated on the basic amount (also, called as the principal amount) borrowed for the entire period at a particular rate of interest. It grows linearly and is preferred for short-term loans. Simple interest is given by,

S.I= (P × R × T) / 100

Amount (A) obtained after calculating the simple interest, is given by,

A = P + S.I

Where,

• A is the amount,
• R is the percentage rate of interest, and
• T is the time duration.
• P is the principal amount, and
• S.I. is the simple interest.

Compound Interest

Compound interest is the interest in which the interest of previous years are added to the principal amount for the calculation of the compound interest. The compound interest grows exponentially, and this is very powerful for long term growth, as it increases the cost of borrowing over time, which can leads to higher interest or higher returns compared to simple interest. Compound interest is given by,

Compound Interest = P (1 + (R / 100))^T – P

Where,

• P is the principal amount,
• R is the rate of interest, and
• T is the time duration.

Amount (A) obtained after calculating the compound interest, is given by,

A = P (1 + (R/N))^NT

Where,

• P is the principal amount,
• R is the annual rate of interest in decimal form,
• N is the number of times the interest is compounded per year, and
• T is the time duration.

In compound interest formula, when interest is compounded annually then amount A is given by,

A = P (1 + (R / 100))^T

In compound interest formula, when interest is compounded half yearly then amount A is given by,

A = P (1 + ((R/2)/ 100))^2T

In compound interest formula, when interest is compounded quarterly then amount A is given by,

A = P (1 + ((R/4)/ 100))^4T

In compound interest formula, when differential rate of interest charged, such that R1% for first year, R2% for second year and R3% for third year, then the amount A is given by,

A = P(1 + (R₁ / 100)) × (1 + (R₂ / 100)) × (1 + (R₃ / 100))

Simple and Compound Interest Practice Questions with solution

These are some important Simple and Compound Interest Questions with Solutions to help you improve your understanding of the concept.

Question 1: A sum of $6000 is deposited into ICICI bank for 4 years. If the bank provides 6%, then what is the amount after the maturity period?

Solution:

Here, P = $6000, R = 6%, T = 4 years.

We know that,

Simple interest = (P × R × T) / 100 = (6000 × 6 × 4) / 100= $1440

Also, Amount is given by the sum of principal amount and simple interest,

Amount = $6000 + $1440 = $7440

Therefore, the amount after the maturity period of 4 years is $7440.

Question 2: An amount of $20000 is deposited in a bank for 2 years. Calculate the interest if rate of interest is 10% compounded annually.

Solution 2:

Here, P = $20000, R = 10%, T = 2 years

Compound Interest is given by,

= P (1 + (R / 100))^T – P

= 20000(1 + (10/100))² – 20000

= 24200 – 20000= $4200

So, the interest obtained is $4200.

Question 3: An amount becomes 10 times in 30 years at simple interest. Calculate the rate of interest given.

Solution:

Given that, T = 30 years

Let, P = y and A = 10y,

Then, S.I = A – P = 10y – y = 9y

We know that, S.I = (P × R × T) / 100

9y = (y × R × 30) / 100

⇒ R = 900y/30y

⇒ R = 30%

Therefore, the rate of interest is 30%.

Question 4: What is the simple interest for five years on a principal amount of $600, if the rate of interest for first 3 years is 10% per annum and rate of interest for another 2 years is 20% per annum?

Solution:

It is Given that, for first 3 years, P₁ = 600, R₁ = 10, T₁ = 3

and for another 2 years, P₂ = 600, R₂ = 20, T₂ = 2

So, Total simple interest = Simple interest for first 3 years + Simple interest for another 2 years

= (P₁ × R₁ × T₁)/100 + (P₂ × R₂ × T₂) / 100 = (600 × 10 × 3)/100 + (600 × 20 × 2)/100

= 180 + 240 = 220

Therefore, the accumulated simple interest in five years is $220.

Question 5: An amount becomes double in 10 years. Find its rate of interest.

Solution:

Let the amount = y,

Since, the amount becomes double in 10 years. So, simple interest, S.I = y

We know that,

S.I = (P × R × T) / 100

⇒ y = (y × R × 10) / 100

We can also write,

R = 100/10 = 10

Therefore, the rate of interest is 10%.

Question 6: If the difference between compound interest and simple interest on some principle amount is at the rate of interest of 20% per annum for 3 years in $48, then what is the principle amount?

Solution:

Here, T = 3 years, R = 20%, P = ?

Also, C.I – S.I = 48

P(1 + (R / 100))^T – P – (P × R × T) / 100 = 48

⇒ P(1 + (20/100))³ – P – (P × 20 × 3) / 100 = 48

⇒ P(6/5)³ – P – P (3/5) = 48

⇒ P ((216/125)³ – 1 – (3/5)) = 48

⇒ P (0.128) = 48

⇒ P = (48/0.128)

⇒ P = 375

Therefore, the principle amount is $375.

Question 7: A sum of money places at compound interest doubles itself in 3 years. In how many years will it amount to 8 times itself?

Solution 7:

Let in 3 years, P = y, C.I = 2y (since, it doubles itself)

Now, by formula,

C.I = P (1 + (R / 100))^T

⇒ 2y = y (1 + (R / 100))³

⇒ 2 = (1 + (R / 100))³

So, (1 + (R/100)) = 2^1/3 . . . (i)

We need to find, T = ? when C.I = 8y,

By formula,

C.I = P (1 + (R / 100))^T

⇒ 8y = y(2^1/3)^T [From equation (i)]

⇒ 2³y = y(2^T/3)

On Comparing, we get

T/3 = 3

⇒ T = 3(3)

⇒ T = 9 years.

Therefore, in 9 years the the sum of money will amount to 8times itself.

Question 8: In how many years will a sum of $800 at 10% per annum compound semi-annually become $926.1 ?

Solution:

Given that, P = $800, R = 10% per year, A = $1064.8, T = ?

By formula, Amount,

A = P (1 + ((R/2)/100))^2T

⇒ 926.1 = 800(1 + (5/100))^2T

⇒ (926.1 /800) = (21 /20)^2T

⇒ (9261 /8000) = (21/20)^2T

⇒ (21/20)³ = (21/10)^2T

On comparing, we get

2T = 3

⇒ T = 3/2 years

Therefore, in 3/2 years the semi-annually compounded sum will become $926.1

Question 9: A tree increases annually by (1/8)^th of its height. By how much will it increase after 2 years, if it stands today 64cm high?

Solution:

The increase% is given by, (1/8) × 100 % = (25/2) %

By formula,

C.I. = P (1 + (R / 100))^T

⇒ C.I.= 64(1 + (25/(2 × 100)))²

⇒ C.I.= 64(9/8)²

⇒ C.I.= 64(81/64)

⇒ C.I.= 81

Therefore, the tree will compound to height 81cms after 2 years.

Question 10: If the compound interest on a certain sum at (50/3)% for 3 years is $1270, what is the simple interest in the same sum at the same rate and for the same period?

Solution:

For compound interest, let P = y, R = (50/3)%, T = 3 years, C.I = $1270

By formula,

C.I.= P(1 + (R/100))^T – P

⇒ 1270 = y(1 + (50/(3*100)))³-y

⇒ 1270 = y(7/6)³-y

⇒ 1270 = ((343/216) – 1)y

⇒ y = 1270/(127/216)

⇒ y = (1270 * 216) / 127

⇒ y = 2160

So, the principle amount is $2160

Now, to calculate simple interest,

S.I. = (P × R × T) / 100

⇒ S.I. = (2160 × (50/3) × 3) / 100

⇒ S.I. = 1080

Therefore, the simple interest is $1080.

Simple Interest Practice Questions

Problem 1: At what rate of simple interest, will a sum of money double itself in 4 years?

Problem 2: A sum of $3200 becomes $3776 in 3 years at a certain rate of simple interest. What is the rate of interest per annum?

Problem 3: What is the simple interest to be paid on a principal of $24000 borrowed at a rate of 15% for a period of 3 years and 6 months?

Problem 4: The simple interest on $30000 at rate of interest 7% per annum for n years is $4200. What is the value of n?

Compound Interest Practice Questions

Question 1: A sum of money doubles itself at some rate of interest of compound interest in 15 years. In how many years will it become eight times of itself with the same rate?

Question 2: $1000 invested on compound interest for 3 years at the rate of interest 10%, 20%, 10% for first, second and third year respectively, then what is the amount after 3 years?

Question 3: A sum becomes $2916 in 2 years at 8% per annum in compound interest. What is the value of sum?

Question 4: A certain sum is invested for a certain time,. It amounts to $3500 at 10% per annum. But, when invested at 8% per annum, it amounts to $3000, then find the time and principle amount.

Question 5: In how many years will $2000 amount to $2420 at the rate of interest of 10% per annum in compound interest?

Question 6: A sum of money on compound interest amounts to $10648 in 3 years and $9680 in 2 years. What is the rate of interest per annum?

Read More,

• Simple Interest
• Simple Interest Calculator
• Compount Interest Formula
• Daily Compound Interest Formula
• Monthly Compound Interest Formula

Simple Interest and Compound Interest- FAQs

What is interest?

The extra money paid for using others money is called interest. In other words, the extra money that we pay to someone with the borrowed money is called interest.

What is sum or principal?

The money borrowed or lent out for a certain period is called the sum or the principal.

It is possible for simple interest to have same value as compound interest? If yes, then when?

Yes, it is possible for simple interest and compound interest to have same value for time period of 1 year.

For which, Simple Interest = Compound Interest = (P × R) / 100.

What is difference between simple interest and compound interest?

The main difference between simple interest and compound interest is that, the simple interest is calculated over the sum or the principal amount whereas, the compound interest is calculated over the principal amount and the interest that has been accumulated to it over time.