Simple and Compound Interest Practice Questions

Simple Interest- It is the interest that is calculated on the basic amount (also called 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- It is the interest in which the interest of previous years is 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 lead to higher interest or higher returns compared to simple interest.

The formula to calculate Compound interest is

A = P(1+\frac{r}{n})^{nt}

C.I. = A - P

Where,

• A represents the total amount of money after compounding,
• P represents the initial amount,
• r is the annual rate of interest,
• n represents the number of times interest is compounded in a year, and
• t represents the number of years.
• C.I. is Compound Interest

Also Check:

• Tricks to Solve Simple Interest
• Tricks to Solve Compound Interest
• Simple Interest Calculator
• Compound Interest Calculator

Practice Questions

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 the rate of interest is 10% compounded annually.
Solution:

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 the first 3 years is 10% per annum and the 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 = 420

Therefore, the accumulated simple interest in five years is $420.

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 placed at compound interest doubles itself in 3 years. In how many years will it amount to 8 times itself?
Solution :

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 and Compound Interest Practice Questions

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

Question 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?

Question 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?

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

Question 5: 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 itself at the same rate?

Question 6: $1000 invested on compound interest for 3 years at the rate of interest 10%, 20%, and 10% for the first, second, and third years, respectively, then what is the amount after 3 years?

Question 7: A sum becomes $2916 in 2 years at 8% per annum in compound interest. What is the value of the sum?

Question 8: 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 principal amount.

Question 9: In how many years will $2000 amount to $2420 at the rate of interest of 10% per annum in compound interest?

Question 10: 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?

Answer Key:

1. Rate of Simple Interest: 25% per annum
2. Rate of Interest per Annum: 6%
3. Simple Interest: $12,600
4. Value of n: 2 years
5. Time to become 8 times (Compound Interest): 45 years
6. Amount after 3 years (Compound Interest): $1452
7. Principal (Sum): $2500
8. Time: 25 years, Principal: $1000
9. Time: 2 years
10. Rate of Interest per Annum: 10%