Interest MCQ Quiz - Objective Question with Answer for Interest - Download Free PDF
Last updated on Jun 5, 2025
Latest Interest MCQ Objective Questions
Interest Question 1:
A sum of ₹9,960 was borrowed at 7.5% per annum compound interest and paid back in two equal annual instalments. What was the amount of each instalment?
Answer (Detailed Solution Below)
Interest Question 1 Detailed Solution
Given
Loan amount = ₹9,960
Interest rate = 7.5% per annum compounded annually
Repayment period = 2 years
Shortcut Trick
Rate of interest = 7.5%
If Principal = 100
Amount = 107.5
So
Principal : Amount = 100 : 107.5 = 40 : 43
So
Principal Installment
First year 40 43
Second year 402 432
Both installments are equal so
Principal Installment
First year 40 × 43 43 × 43
Second year 402 432
So
Total Principal = 40 × 43 + 402 = 3320
3320 units = Rs. 9960
1 unit = 3
so
Installment = 432 × 3 = Rs. 5547
Interest Question 2:
P invests Rs (X − 5000) at a compound interest rate of R% per annum for 2 years, while Q invests Rs (X + 2000) at 2R% per annum for the same period. The ratio of their investments is given to be 5 : 7. Find the difference in the compound interest earned by A and B after 2 years.
Answer (Detailed Solution Below)
Interest Question 2 Detailed Solution
Calculation
So, [ X – 5000] / [ X + 2000] = 5 /7
Or, 5𝑋 + 10000 = 7X – 35000
Or, 2𝑋 = 45000
Or, 𝑋 = 22500
So, Investment of P and Q is Rs 17500 and Rs 24500 respectively.
We don’t know the value of R So, answer can’t be determined.
(d) Can’t be determined
Interest Question 3:
A principal amount is invested at 12% per annum simple interest for a period of 4 years, 11 months, and 28 days in a scheme. The total amount received from this scheme is then invested for 2 years and 2 days in another scheme at 20% per annum compound interest. The compound interest earned from the second scheme is Rs. 1056.4. Find the approximate amount initially invested in the first scheme?
Answer (Detailed Solution Below)
Interest Question 3 Detailed Solution
Calculation
We should take approx. values
So, four years 11 months and 28 days = 5 years
Two years 2 days = 2 years
And 1056.4 Rs = 1056
Equivalent rate of interest at rate of 20% p.a. for two years on compound
interest annually = (20 + 20 + ( 20 × 20) / 100 )% = 44%
Let amount invested in first scheme = 100x
So, amount invested in second scheme = 100x + 100x × (12× 5) /100
= 160x
ATQ, 160x × (44 / 100) = 1056
Or, 1.6x = 24
x = 15
So, 100x = 1500
Interest Question 4:
A principal amount of ₹1200 grows to ₹1440 in 2 years. Calculate the rate of interest.
Answer (Detailed Solution Below)
Interest Question 4 Detailed Solution
Given:
Principal (P) = ₹1200
Amount (A) = ₹1440
Time (t) = 2 years
Formula Used:
Simple Interest (SI) = A - P
SI = \(\dfrac{P \times r \times t}{100}\)
Where, r = rate of interest
Calculations:
SI = \(\dfrac{P \times r \times t}{100}\):
240 = \(\dfrac{1200 \times r \times 2}{100}\)
⇒ 240 = 12 × r × 2
⇒ 240 = 24 × r
⇒ r = \(\dfrac{240}{24}\)
⇒ r = 10%
∴ The rate of interest is 10% per annum.
Interest Question 5:
A principal amount earns Rs. 420 as simple interest at an annual rate of 10% over 2 years. Calculate the principal amount.
Answer (Detailed Solution Below)
Interest Question 5 Detailed Solution
Given:
Simple Interest (SI) = ₹420
Annual Rate of Interest (R) = 10%
Time (T) = 2 years
Formula Used:
Simple Interest (SI) = (Principal (P) × Rate (R) × Time (T)) / 100
To find the Principal (P), rearrange the formula: P = (SI × 100) / (R × T)
Calculation:
P = (420 × 100) / (10 × 2)
P = 42000 / 20
P = 2100
∴ The principal amount is ₹2100.
Top Interest MCQ Objective Questions
On a certain sum of money, the compound interest for 2 years is Rs. 304.5 and the simple interest for the same period of time is Rs. 290. The rate of interest per annum:
Answer (Detailed Solution Below)
Interest Question 6 Detailed Solution
Download Solution PDFGiven:
C.I for 2 years = Rs. 304.5
S.I for 2 years = Rs. 290
Calculation:
S.I for 1 year = Rs. (290/2) = Rs. 145
Difference between S.I and C.I = Rs. (304.5 – 290)
⇒ Rs. 14.5
Rate of interest per annum = (14.5/145) × 100%
⇒ 10%
∴ The rate of interest per annum is 10%Find the principal if the interest compounded at the rate of 12% per annum, compounding annually for 2 years is Rs. 1,908.
Answer (Detailed Solution Below)
Interest Question 7 Detailed Solution
Download Solution PDFGiven
Compound interest after 2 years = Rs. 1,908
Rate of interest = 12% per annum
Concept:
CI = P [(1 + r/100)t - 1]
Solution:
CI = P [(1 + r/100)t - 1]
⇒ 1908 = P [(1 + 12/100)2 - 1]
⇒ 1908 = P [(1 + 3/25)2 - 1]
⇒ 1908 = P [(28/25)2 - 1]
⇒ 1908 = P [784/625 - 1]
⇒ 1908 = P × 159 / 625
⇒ P = 1908 × 625 / 159
⇒ P = 12 × 625 = Rs. 7500
Hence, the principal is Rs. 7,500.
A sum becomes 27 times in 3 years, compounded annually at a certain rate of interest. Calculate annual interest rate.
Answer (Detailed Solution Below)
Interest Question 8 Detailed Solution
Download Solution PDFGiven:
Amount = 27 P in 3 years
Concept:
In compound interest, the ratio of the amount and the principal is given by:
\(\frac{A}{P} = (1 + \frac{R}{100})^n\)
Calculation:
We know that,
\(\frac{A}{P} = (1 + \frac{R}{100})^n\)
\(⇒ \frac{27}{1} = (1 + \frac{R}{100})^3 \)
\(⇒ 3^3 = (1 + \frac{R}{100})^3 \)
\(⇒ 3 = (1 + \frac{R}{100}) \)
⇒ R/100 = 3 - 1 = 2
⇒ R = 200%
Hence, the annual interest rate is 200%.
Shortcut Trick
A sum becomes 27 times in 3 years
3x = 27
⇒ 3x = 33
⇒ x = 3
Rate = (x - 1) × 100%
⇒ (3 - 1) × 100% = 200%
∴ The annual interest rate is 200%.
A sum of money invested at a certain rate of simple interest per annum amounts to Rs. 14,522 in seven years and to Rs. 18,906 in eleven years. Find the sum invested (in Rs.).
Answer (Detailed Solution Below)
Interest Question 9 Detailed Solution
Download Solution PDFGiven:
Amount produce in 7 years = Rs.14522
Amount produce in 11 years = Rs.18906
Formula used:
Simple interest (S.I) = (P × R × T)/100
Calculation:
Amount produce in 7 years = Rs.14522
Amount produce in 11 years = Rs.18906
S.I produced in (11 - 7) = 4 years = (18906 - 14522) = Rs.4384
S.I in 1 years = 4384/4 = 1096
Principal = 14522 - (1096 × 7)
⇒ (14522 - 7672) = Rs.6850
∴ The correct answer is Rs.6850.
A sum becomes Rs. 10650 in 5 years. and Rs. 11076 in 6 years at simple interest. What is the sum?
Answer (Detailed Solution Below)
Interest Question 10 Detailed Solution
Download Solution PDFConcept Used:
In this type of question, number can be calculated by using the below formulae
Formula Used:
If a sum with simple interest rate, amounts to Rs. ‘A’ in y years. and Rs. ‘B’ in z years. then,
P = (A × z – B × y)/(z – y)
Calculation:
Using the above formulae, we have
⇒ P = (10650 × 6 – 11076 × 5)
⇒ P = Rs. 8520
∴ Required principal is Rs. 8520
A sum becomes Rs. 10650 in 5 years. and Rs. 11076 in 6 years. at simple interest
Interest of 1 year = 11076 – 10650 = Rs. 426
Interest of 5 year = 426 × 5 = 2130
∴ Required principal = 10650 – 2130 = Rs. 8520
What is the difference (in Rs.) between the simple interest and the compound interest on a sum of Rs. 8000 for \(2\frac{2}{5}\) years at the rate of 10% p.a. when the interest is compounded yearly?
Answer (Detailed Solution Below)
Interest Question 11 Detailed Solution
Download Solution PDFGiven:
Principal = Rs. 8000
Rate = 10%
Time = \(2\frac{2}{5}\) years
Formula used:
SI = (P × t × r)/100
CI = P(1 + r/100)t - P
P = Principal
t = time
r = rate
Calculation:
SI = (8000 × 12 × 10)/(100 × 5)
⇒ Rs. 1920
CI = 8000[1 + 10/100]2 × [1 + 4/100] - 8000
⇒ 8000 × 11/10 × 11/10 × 26/25 - 8000
⇒ 10067.2 - 8000
⇒ 2067.2
Difference = 2067.2 - 1920 = 147.2
∴ Required difference is Rs. 147.2
Shortcut Trick
So, the difference of CI and SI = 80 + 32 + 32 + 3.2
∴ The Difference of CI and SI = 147.2.
Rs. 15,000 will amount to Rs. 19,965 in 15 months at ______ per annum and the compund interest is calculated on every 5 months.
Answer (Detailed Solution Below)
Interest Question 12 Detailed Solution
Download Solution PDFGiven:
Principal = Rs. 15,000
Amount = Rs. 19,965
Time = 15 months
Condition = on every 5 months
Concept used:
Condition = on every 5 months
New rate = Rate × 5/12
New time = Time × 12/5
Calculations:
Let the new rate be R%
According to the question,
New time = Time × 12/5
⇒ 15 × 12/5 = 36 months = 3 years
Simplifying the values by dividing it by 15 to its lowest possible values, we get Principal = 1000 and Amount = 1331
Now, new time period is 3 years, hence taking the cube roots of Principal and Amount,
⇒ R = 10%
New rate = Rate × 5/12
⇒ 10 = Rate × 5/12
⇒ Rate = (10 × 12)/5
⇒ Rate = 24%
∴ Rate is 24% per annum.
Alternate MethodGiven:
Principal = Rs. 15,000
Amount = Rs. 19,965
Time = 15 months
Condition = on every 5 months
Concept used:
Condition = on every 5 months
New rate = Rate × 5/12
New time = Time × 12/5
Formulae used:
(1) Effective rate for 3 years = 3R + 3R2/100 + R3/10000
(2) A = P(1 + R/100)T
Where, A → Amount
P → Principal
R → Rate of interest
T → Time
Calculations:
According to the question,
Let the new rate be R%
New time = Time × 12/5
⇒ 15 × 12/5 = 36 months = 3 years
Amount = P(1 + R/100)T
⇒ 19,965 = 15,000(1 + R/100)3
⇒ 19,965/15,000 = (1 + R/100)3
⇒ 1331/1000 = (1 + R/100)3
⇒ (11/10)3 = (1 + R/100)3
⇒ 11/10 = 1 + R/100
⇒ (11/10) – 1 = R/100
⇒ 1/10 = R/100
⇒ R = 10%
New rate = Rate × 5/12
⇒ 10 = Rate × 5/12
⇒ Rate = (10 × 12)/5
⇒ Rate = 24%
∴ Rate is 24% per annum
Additional InformationCompound Interest means interest earned on interest. Simple interest always occurs on only principal but compound interest also occurs on simple interest. So, if time period is 2 years, compound interest will also apply on simple interest of first year.
A sum of money at simple interest doubles in 10 years. In how many years, at the same rate, will it be tripled?
Answer (Detailed Solution Below)
Interest Question 13 Detailed Solution
Download Solution PDFGiven:
Amount = 2P
Time = 10 years
Formula used:
SI = (PRT/100)
Amount = (PRT/100) + P
Calculation:
Amount = (PRT/100) + P
2P = (PR/10) + P
⇒ P = (PR/10)
⇒ R = 10%
According to the question, Amount = 3P
3P = (10PT/100) + P
⇒ 2P = (PT/10)
⇒ T = 20 years
∴ Time taken to triple the amount is 20 years.
Shortcut TrickInterest = 2P - P = P = 100% of principle
Time = 10 year
Hence, rate = Interest/Time = 100/10 = 10%
New interest = 3P - P = 2P = 200% of principle
∴ Time = Interest/Rate = 200/10 = 20 Years
A sum of money was invested at the rate of 7.5% simple interest per annuum for 4 years. If the investments were for 5 years, the interest earned would have been Rs. 375 more. What was the initial sum invested?
Answer (Detailed Solution Below)
Interest Question 14 Detailed Solution
Download Solution PDFInterest earned for 5 years – Interest earned for 4 years = 375
Let the principal be Rs. P,
⇒ (P × 7.5 × 5) /100 – (P × 7.5 × 4) /100 = 375
⇒ (37.5 × P) /100 – (30 × P) /100 = 375
⇒ (7.5 × P) /100 = 375
∴ P = Rs. 5000A sum of money lent out at simple interest amounts to Rs. 715 after 3 years and to Rs. 990 after a further period of 5 years. Find the sum.
Answer (Detailed Solution Below)
Interest Question 15 Detailed Solution
Download Solution PDFGiven:
Amount after 3 years = Rs. 715
Amount after 8 years = Rs. 990
Formula used:
A = P + SI
Where A = amount , P = Principle
And SI = Simple interest
Calculation:
Amount in 3 years = Rs. 715
Now it is given in the question, amount for the time of further 5 years i.e
Total time = 5 years + 3 years = 8 years.
Amount in 8 years = Rs. 990
SI for 5 years = Amount after 8 years - Amount after 3 years
⇒ SI for 5 years = 990 - 715 = 275
SI for 1 years = 275/5 = 55
SI for 3 years = 55 × 3 = Rs.165
P = Amount of 3 years - SI of 3 years
⇒ P = 715 - 165 = 550
∴ The sum is Rs. 550
Confusion Points It is given in the question that after further 5 years amount is calculated , so total time will be (5 +3) years = 8 years. not 5 years.