Simple and Compound Both MCQ Quiz - Objective Question with Answer for Simple and Compound Both - Download Free PDF
Last updated on Jun 3, 2025
Latest Simple and Compound Both MCQ Objective Questions
Simple and Compound Both Question 1:
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)
Simple and Compound Both Question 1 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
Simple and Compound Both Question 2:
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)
Simple and Compound Both Question 2 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
Simple and Compound Both Question 3:
Simple interest received on a certain sum at a rate of simple interest of 5% for 2 years is Rs.780. If the rate of interest remains same, what will be the total amount at the time of withdrawal at the end of 5 years.
Answer (Detailed Solution Below)
Simple and Compound Both Question 3 Detailed Solution
Calculation
We use the simple interest formula:
SI = (P × R × T)/100
Given:
SI = 780, R = 5%, T = 2
→ 780=P×5×2100
→ P=780×100/10=7800
Now SI for 5 years:
→ SI=7800×5×5/100=1950
Total amount = Principal + SI = 7800 + 1950 = Rs.9750
Simple and Compound Both Question 4:
A sum amounts to ₹ 9075 in \(1\frac{1}{3}\) years at 15% p.a. compounded 8-monthly. What is the simple interest (in ₹) on the same sum for the same period and at the same rate of interest ?
Answer (Detailed Solution Below)
Simple and Compound Both Question 4 Detailed Solution
Given:
Amount (A) = ₹ 9075
Time (T) = 1 and 1/3 years = 4/3 years
Rate of interest (R) = 15% p.a.
Compounded 8-monthly
Formula used:
For compound interest: A = P(1 + r/100)n, where:
A = Amount
P = Principal
r = Rate of interest per compounding period
n = Number of compounding periods
Calculation:
First, calculate the number of compounding periods (n) and the rate per compounding period (r).
Time in months = (4/3) years × 12 months/year = 16 months
Compounding period = 8 months
Number of compounding periods (n) = Total months / Compounding period = 16 / 8 = 2 periods
Annual rate = 15%
Rate per month = 15% / 12 = 5/4 %
Rate per 8-monthly period (r) = (5/4) % × 8 = 10%
Now, use the compound interest formula to find the Principal (P):
A = P(1 + r/100)n
9075 = P(1 + 10/100)2
9075 = P(1 + 1/10)2
9075 = P(11/10)2
9075 = P(121/100)
P = (9075 × 100) / 121
P = 75 × 100
P = ₹ 7500
SI on the same sum (P = ₹ 7500) for the same period (T = 4/3 years) and at the same rate (R = 15% p.a.).
SI = (P × R × T) / 100
SI = (7500 × 15 × (4/3)) / 100
SI = (7500 × 15 × 4) / (3 × 100)
SI = (75 × 15 × 4) / 3
SI = 25 × 15 × 4
SI = 25 × 60
SI = ₹ 1500
∴ The correct answer is option 3.
Simple and Compound Both Question 5:
The difference between compound interest and simple interest on an amount of money in three years at the rate of 8% is Rs. 3,456. Then the principal amount is
Answer (Detailed Solution Below)
Simple and Compound Both Question 5 Detailed Solution
Given:
Difference between CI and SI for 3 years = ₹3,456
Rate of interest (r) = 8% per annum
Time (t) = 3 years
Formula Used:
Difference between CI and SI for 3 years = P × (r/100)2 × (3 + r/100)
Where P is the principal.
Calculation:
Substitute the given values into the formula:
3456 = P × (8/100)2 × (3 + 8/100)
3456 = P × (0.08)2 × (3 + 0.08)
3456 = P × 0.0064 × 3.08
3456 = P × 0.019712
P = 3456 / 0.019712
P = 175324.625 ≈ 175325
∴ The principal amount is approximately ₹175,325.
Top Simple and Compound Both 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)
Simple and Compound Both 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)
Simple and Compound Both 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.
The simple interest on a certain principal amount for 4 years at 10% per annum is half of the compound interest on Rs. 1000 for 2 years at 20% per annum. Find the principal amount
Answer (Detailed Solution Below)
Simple and Compound Both Question 8 Detailed Solution
Download Solution PDFCalculation:
The effective rate of 20% for 2years is = 20 + 20 + (20 × 20)/100 = 44%
So, C.I on 1000 for 2 years is = 1000 × 44/100 = 440
Let the principal invest in S.I be P
Now, according to the question,
(P × 4 × 10)/100 = 440/2
⇒ P = 1100/2 = 550
∴ The principal amount be 550
The difference between the simple interest and compound interest (interest is compounded half yearly) on a sum at the rate of 25% per annum for one year is ₹ 4375. What will be the principal?
Answer (Detailed Solution Below)
Simple and Compound Both Question 9 Detailed Solution
Download Solution PDFGiven:
The difference between the simple interest and compound interest (interest is compounded half yearly) on a sum at the rate of 25% per annum for one year is ₹ 4375
Formula used:
Simple Interest = (P × N × R)/100
Compound Interest = [P(1 + (r/200))T] - P (for compounded half yearly)
Calculation:
Let P be the Principal,
S.I = (P × 1 × 25)/100 = P/4
C.I = [P(1 + (25/200))2] - P ( T = 2 ∵ compounded half yearly for 1 year)
⇒ C.I = 17P/64
Now, C.I - S.I = (17P/64) - (P/4) = P/64
⇒ P/64 = 4375
∴ P = 64 × 4375 = 280000
Shortcut TrickFormula used:
CI - SI = P(R/100)2
Rate (R) = 25%/2 due to the compounded half-yearly.
⇒ 4375 = P (25/200)2
⇒ P = 4375 × 64
⇒ P = 280,000
∴ The sum is Rs. 280,000.
The simple interest on a certain sum of ₹ P at a rate of r% per annum for 3 years is Rs.11,250 and the compound interest on the same sum for 2 years at the same rate percent p.a. is ₹ 7,650. What is the value of P and r, respectively?
Answer (Detailed Solution Below)
Simple and Compound Both Question 10 Detailed Solution
Download Solution PDFGiven data:
SI for 3 years = Rs 11,250
CI for 2 years at the same rate = Rs 7650
Formula used:
P = \(SI\times 100\over {R\times T}\) where-
P = Principal
SI = Simple Interest
R = Rate
T = Time
Calculation:
SI for 1 year = 11,250 ÷ 3 = Rs 3,750
SI for 2 year = 2 × 3750 = Rs 7500
Difference between CI and SI for 2 year = 7650 - 7500 = Rs 150
⇒ This difference between CI and SI was on the SI for the 1st year i.e., Rs 3750
∴ Rate % = \(150\over 3750\) × 100 = 4%
Principal = \(3750\times 100\over {1\times4}\) = Rs 93,750
∴ The Principal amount was Rs 93,750 and the rate of interest was 4%.
The difference between the compound interest and the simple interest accrued on an amount of ₹40,000 in 2 years was ₹324. The rate of interest per annum was:
Answer (Detailed Solution Below)
Simple and Compound Both Question 11 Detailed Solution
Download Solution PDFGiven:-
CI - SI = 324
Principal = 40000, Time = 2 years
Formula used:-
Compound Interest = Amount - Principal
CI = P[(1 + R/100)n - 1]
Simple interest = (P × R × T)/100
Calculation:-
According to question-
⇒ P[(1 + R/100)n - 1] - (P × R × T)/100 = 324
⇒ 40000 [(1 + R/100)2 - 1] - (40000 × R × 2)/100 = 324
⇒ 40000 [{(100 + R)2/1002 - 1} - {R × 2}/100 = 324
⇒ 400 [{1002 + R2 + 2 × 100 × R -1002}/100 - 2R] = 324
⇒ [{R2 + 200R}/100 - 2R] = 324/400
⇒ (R2 + 200R - 200R)/100 = 324/400
⇒ R2 = 32400/400
⇒ R2 = 81 = 9%
∴ The rate of interest per annum is 9%.
Shortcut TrickFormula used:-
Difference between CI - SI for 2 years,
⇒ D = P(R/100)2
Where,
D = Difference, P = Principal, R = Rate of interest
Calculation:-
⇒ 324 = 40000(R/100)2
⇒ R2 × 40000 = 3240000
⇒ R2 = 81
⇒ R = 9%
∴ Required rate of interest is 9%.
If the simple interest for 2 years is Rs. 500 at 10% rate of interest. Find the compound interest for the same time.
Answer (Detailed Solution Below)
Simple and Compound Both Question 12 Detailed Solution
Download Solution PDFGiven:
Time = 2 years, Simple Interest = 500, rate = 10%
Formula used:
Simple Interest = (Principal × Rate × Time)/100
Compound Interest = Principal[(1 + rate/100)t – 1]
Calculation:
Let the principal be ‘P’.
Simple Interest = (Principal × Rate × Time)/100
⇒ 500 = (Principal × 10 × 2)/100
⇒ Principal = 2500
Compound Interest = Principal[(1 + rate/100)t – 1]
⇒ 2500[(1 + 10/100)2 – 1]
⇒ 525
∴ The compound Interest is Rs 525.
On a sum of money, the compound interest for 2 years is Rs. 832, while the simple interest for the same time period is Rs.800, then find out the difference amount for period of 3 years?
Answer (Detailed Solution Below)
Simple and Compound Both Question 13 Detailed Solution
Download Solution PDF
|
1st |
2nd |
|
SI |
400 |
400 |
400 |
CI |
400 |
432 |
432+432×8/100 |
Rate = 32/400 × 100 = 8%
Total SI for 3 years = 1200
Total CI for 3 years = 1298.56
∴ Difference = 98.56
The difference in compound interest, under annual compounding, and simple interest on a certain sum at the same rate of interest in 2 years is 144% of the sum. Find the rate of interest per annum.
Answer (Detailed Solution Below)
Simple and Compound Both Question 14 Detailed Solution
Download Solution PDFGiven data:
The difference between Compound Interest (CI) and Simple Interest (SI) for 2 years = 144% of the principal (P)
Concept or formula:
Difference between CI and SI for 2 years is given by P × (r ÷ 100)2
Calculation:
Substitute the given values in the formula
⇒ 144% P = P × (r ÷ 100)2
⇒ (144/100)P = P × (R/100)2
Taking square root on both sides,
⇒ 12/10 = R/100
⇒ R = 120
Hence, the rate of interest per annum is 120%.
What is the difference between the compound interest and the simple interest on a sum of Rs. 4500 for 3 years at the rate of 8% per annum?
Answer (Detailed Solution Below)
Simple and Compound Both Question 15 Detailed Solution
Download Solution PDFHere P = 4500 , T = 8 , R = 8%
Simple interest = (P × R × T)/100, where P is the principal, R is the rate of interest and T is the time period.
Compound interest = [P (1 + R/100)n] - P, where P is the principal, R is the rate of interest and n is the time period.
⇒ SI = (4500 × 8 × 3)/100 = Rs. 1080
⇒ CI = [4500 (1 + 8/100)3] - 4500 = Rs. 5668.7 - 4500 = 1168.7
∴ Required difference = Rs. 88.70