Simple interest questions are available here to help students learn the formula and how to apply the simple interest formula in various problems, including real-life scenarios. We know that “interest” is the most commonly used word when dealing with financial matters. Also, different types of interests exist, such as simple interest, compound interest, etc. In this article, you will get solved and practice questions on simple interest that cover all possible applications of simple interest.
What is the simple interest formula?
Simple Interest (SI) calculates the amount of interest for a certain principal amount of money at some interest rate and for a given period of time.
The formula of simple interest is given by:
SI = PTR/100
Here,
P = Principal amount
T = Time (in years)
R = Interest rate
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Simple Interest Questions and Answers
1. Given that simple interest on a certain sum of money is Rs. 4016.25 at 9% per annum in 5 years. Find the sum of money.
Solution:
Let P be the principal amount or sum of money.
Time (T) = 5 years
Rate of interest (R) = 9%
Simple interest earned (SI) = Rs. 4016.25
As we know,
SI = PTR/100
Rs. 4016.25 = (P × 5 × 9)/100
P = (Rs. 4016.25 × 100)/(5 × 9)
= Rs. 8925
Therefore, the sum of money is Rs. 8925.
2. Calculate the simple interest on Rs. 8000 for 15 months at 6 paise per rupee per month.
Solution:
Given,
Principal amount (P) = Rs. 8000
Time (T) = 15 months
Rate (R) = 6 paise per rupee per month
Here, the rate of interest and the time are given per month.
So, we can use the simple interest formula as:
SI = PTR/100
= (Rs. 8000 × 15 × 6)/100
= Rs. 7200
Therefore, the simple interest is Rs. 7200.
3. A sum of Rs. 25000 will become Rs. 31000 in 48 months at some rate of simple interest. Find the rate of interest per annum.
Solution:
Given,
Principal amount (P) = Rs. 25000
Time (T) = 48 months = (48/12) years = 4 years
Total amount after 4 years (A) = Rs. 31000
Let R be the rate of interest.
As we know,
A = P + SI
Rs. 31000 = Rs. 25000 + [(Rs. 25000 × 4 × R)/100]
Rs. 31000 – Rs. 25000 = Rs. 1000 × R
R = Rs. 6000/Rs. 1000 = 6
Therefore, the rate of interest per annum is 6%.
4. A sum of Rs. 12000 is lent out at 5% per annum simple interest for 5 years. What will be the amount after 5 years?
Solution:
Given,
Principal amount (P) = Rs. 12000
Rate of interest per annum (R) = 5%
Time (T) = 5 years
SI = PTR/100
= (Rs. 12000 × 5 × 5)/100
= Rs. 3000
Thus, the total amount after 5 years = P + SI
= Rs. 12000 + Rs. 3000
= Rs. 15000
5. A sum of Rs 1750 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. What is the interest accumulated on each part (in Rs)?
Solution:
Given,
Principal (P) = Rs. 1750
Let x be the first part of the sum.
So, the second part will be (Rs. 1750 – x).
We know that SI = PTR/100
According to the given,
⇒ (x × 8 × 1)/100 = [(1750 – x) × 6 × 1]/100
⇒ 8x = (1750 – x) × 6
⇒ 4x = 5250 − 3x
⇒ 7x = 5250
⇒ x = 750
Therefore, the first part of the sum = Rs. 750
Second part of the sum = Rs. (1750 – 750) = Rs. 1000
Hence, the interest on each part = Rs. 750 × (8/100) = Rs. 60
6. A person deposited some amount of money in the bank at simple interest. After 15 years, the amount became seven times. In how many years will the amount become ten times if the interest rate remains the same?
Solution:
Let P be the amount of money deposited in the bank.
And let R be the rate of interest per annum.
Time = 15 years
According to the given,
7P = P + (P × 15 × R)/100
7P – P = 15PR/100
6P = 15PR/100
⇒ R = (6P × 100)/15P
⇒ R = 40
Thus, the rate of interest is 40%.
Let T be the number of years in which the amount P becomes 10 times.
So, 10P = P + (P × T × 40)/100
10P – P = 2PT/5
9P = 2PT/5
⇒ T = (9P × 5)/2P
T = 22.5
Therefore, in 22.5 years, the amount will be 10 times the initial deposit.
7. A sum of Rs. 800 amounts to Rs. 920 in 3 years at simple interest. If the interest rate increases by 3%, what will be the amount?
Solution:
Given,
Principal (P) = Rs. 800
Time (T) = 3 years
Amount after 3 years (A) = Rs. 920
SI = A – P
= Rs. 920 – Rs. 800
= Rs. 120
Let R be the rate of interest.
Using the simple interest formula,
Rs. 120 = (Rs. 800 × 3 × R)/100
Rs. 12000 = Rs. 2400 × R
R = 5
Thus, the rate of interest is 5%.
New interest rate = (5 + 3)% = 8%
New simple interest = (Rs. 800 × 3 × 8)/100
= Rs. 192
New amount = Principle + New simple interest
= Rs. 800 + Rs. 192
= Rs. 992
8. A sum of money was lent at simple interest at 11% per annum for 7/2 years and 9/2 years, respectively. If the interest difference for two periods was Rs. 5500, find the sum.
Solution:
Let P be the sum of money lent.
Given,
Rate of interest per annum (R) = 11%
Interest earned in 9/2 years – Interest earned in 7/2 years = Rs. 5500
Using simple interest formula, we have;
P × (9/2) × 11 × (1/100) – P × (7/2) × 11 × (1/100) = Rs. 5500
(P/200) [99 – 77] = Rs. 5500
22P/200 = Rs. 5500
P = (Rs. 5500 × 200)/22
= Rs. 50000
Therefore, the required sum is Rs. 50000.
9. Rs. 2379 is divided into 3 parts so that the amounts after 2, 3 and 4 years, respectively, are equal. What is the first part if the interest rate is 5% per annum on simple interest?
Solution:
Given that a sum of money Rs. 2379 is divided into three parts.
Rate of interest (R) = 5%
Let a, b, and c be the three parts.
As we know, SI = PTR/100
According to the given,
a + (a × 2 × 5/100) = b + (b × 3 × 5/100) = c + (c × 4 × 5/100)
a + (a/10) = b + (3b/20) = c + (c/5)
11a/10 = 23b/20 = 6c/5
Let 11a/10 = 23b/20 = 6c/5 = k
Thus, a = 10k/11, b = 20k/23, c = 5k/6
Also,
a + b + c = Rs. 2379
(10k/11) + (20k/23) + (5k/6) = 2379
(10k × 23 × 6) + (20k × 11 × 6) + (5k × 11 × 23) = 2379 × 11 × 23 × 6
1380k + 1320k + 1265k = 2379 × 11 × 23 × 6
⇒ 3965k = 2379 × 11 × 23 × 6
⇒ k = (2379 × 11 × 23 × 6)/3965
Now, x = 10k/11 = (2379 × 11 × 23 × 6 × 10)/ (3965 × 11) = 828
Therefore, the first part of the sum is Rs. 828.
10. A simple interest of Rs. 2500 is earned by investing a sum of money for 13 years. The interest rate is charged at 4% for the first 3 years, 5% for the next 4 years and 8% beyond 7 years. Find the sum of money invested.
Solution:
Let P be the sum of money invested.
Interest rate for the first 3 years = 4%
Interest rate for the next 4 years = 5%
Interest rate beyond 7 years, i.e. for (13 – 7) = 6 years = 8%
Using the simple interest formula, we have;
(P × 3 × 4/100) + (P × 4 × 5/100) + (P × 6 × 8/100) = Rs. 2500
12P + 20P + 48P = Rs. 2500 × 100
80P = Rs. 250000
P = Rs. 250000/80 = Rs. 3125
Therefore, the sum of money invested is Rs. 3125.
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Practice Questions on Simple Interest
- What will be the ratio of simple interest earned by a certain amount at the same interest rate for 4 years and that for 12 years?
- A sum of money amounts to Rs. 1008 in two years and to Rs. 1164 in three and half years. Estimate the sum and the rate of interest.
- Suppose you borrowed Rs. 10,000 from the bank at a 13% rate for 4 years. Find the interest you will pay on this loan.
- What will be simple interest for 1 yr and 8 months on a sum of Rs. 28500 at the rate of 12% per annum?
- The simple interest on a sum of money will be Rs.6000 after ten years. If the principal is triple after five years, what will be the total interest at the end of the tenth year?
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