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All questions of Simple & Compound Interest for UGC NET Exam

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Can you explain the answer of this question below:
A sum of money amounts to Rs.9800 after 5 years and Rs.12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
  • A:15%
  • B:12%
  • C:8%
  • D:5%

The answer is B.

Arya Roy answered
We can get SI of 3 years = 12005 - 9800 = 2205

SI for 5 years = (2205/3)*5 = 3675 [so that we can get principal amount after deducting SI]

Principal = 12005 - 3675 = 6125 

So Rate = (100*3675)/(6125*5) = 12%

Arun took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If he paid Rs.686 as interest at the end of the loan period, what was the rate of interest?
  • a)
    8%
  • b)
    6%
  • c)
    4%
  • d)
    7%
Correct answer is option 'D'. Can you explain this answer?

Meghana Mishra answered
Simple Interest (SI) = P N R / 100
P is the Principal loan amount = Rs.1400
N is the number of years of deposit
R is the rate of interest
It is given that the loan period is as many years as the rate of interest.
So, N = R
Interest at the end of the loan period (SI ) = Rs.686
So,
686 = 1400 * R * R /100
R^2 = 686*100 /1400
R^2 = 49
R = 7%

The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is
  • a)
    5
  • b)
    4
  • c)
    6
  • d)
    2
Correct answer is option 'B'. Can you explain this answer?

Anaya Patel answered
P [1 + (r/100)]n  >  2P
⇒ P [1 + (20/100)]n  >  2P
[1 + (2/10) ]n  > 2
[12 / 10]n  > 2
[6/5]n  > 2
{6/5 * 6/5 * 6/5 * 6/5}  >  2
∴ n = 4
 

What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.? 
  • a)
    Rs. 14705.24
  • b)
    Rs. 14602.25
  • c)
    Rs. 14822.26
  • d)
    Rs. 14322.10
Correct answer is option 'A'. Can you explain this answer?

Rhea Reddy answered
Amount after 3 years = P(1 + R/100)T
=> 40000(1 + 11/100)3
=> 40000(111/100)3
=> 40000[(111*111*111)/(100*100*100)]
=> (4*111*111*111)/100 
=> 54705.24
Compound Interest = 54705.24 - 40000 
= Rs. 14705.24

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is: 
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    3.5
Correct answer is option 'B'. Can you explain this answer?

Raghavendra Sharma answered
Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years.
Then, 30000 (1 + 7/100)^n = 34347
= (107/100)^n = 34347/30000 = 11449/10000 = (107/100)^2
n = 2 years.

The Simple interest on a certain sum for 2 years at 20% per annum is Rs. 80. The corresponding compound interest is 
  • a)
    Rs. 66
  • b)
    Rs. 82
  • c)
    Rs. 86
  • d)
    Rs. 88
Correct answer is option 'D'. Can you explain this answer?

Savitri Verma answered
Time =2. rate =20%. p=? SI =80
p=SI*100/R*T p=80×100/20×2
p=200. A=p(1+R/100)^n
A=200(1+20/100)^2
A=200×12×12/100×100
A=288
( CI=A-P)
CI =288-200 = 88

If a sum of Rs. 9 is lent to be paid back in 10 equal monthly installments of re. 1 each, then the rate of interest is
  • a)
    11.33%
  • b)
    11%
  • c)
    266.67%
  • d)
    33.33%
Correct answer is option 'D'. Can you explain this answer?

Manoj Ghosh answered
Let's try to understand the problem step by step.

A sum of Rs. 9 is lent to be paid back in 10 equal monthly installments of Re. 1 each.

This means that the borrower is paying back Re. 1 per month for 10 months.

Now, let's calculate the interest paid in each installment.

1. In the first month, the borrower still owes Rs. 9, so no interest is paid.
2. In the second month, the borrower has already paid Re. 1, so he now owes Rs. 8. The interest paid would be on Rs. 8.
3. In the third month, the borrower has paid Rs. 2, so he now owes Rs. 7. The interest paid would be on Rs. 7.
4. This continues until the 10th month when the borrower has paid Rs. 9 and owes nothing.

Now let's calculate the total interest paid over the 10 months.

Total Interest Paid = (Interest on Rs. 8) + (Interest on Rs. 7) + ... + (Interest on Re. 1)

Let's assume the rate of interest is "R" percent per month.

Total Interest Paid = (8 * R) + (7 * R) + ... + (1 * R)

Now, we know that the total amount paid is Rs. 10 (10 installments of Re. 1 each), and the total amount lent is Rs. 9. So, the total interest paid is Rs. 1.

1 = (8 * R) + (7 * R) + ... + (1 * R)

Now we can simplify the equation:

1 = R * (8 + 7 + 6 + 5 + 4 + 3 + 2 + 1)

1 = R * 36

Now, let's find the value of R (the rate of interest per month):

R = 1/36

Since we need to calculate the rate of interest in percentage, we multiply R by 100:

R (%) = (1/36) * 100 = 2.78%

Now, we have the monthly rate of interest. To find the annual rate of interest, we multiply the monthly rate by 12:

Annual Rate of Interest = 2.78% * 12 = 33.33%

What annual payment will discharge a debt of Rs. 6450 due in 5 years at 10% per annum?
  • a)
    Rs.1075
  • b)
    Rs.1050
  • c)
    Rs.1100
  • d)
    Rs.1025
Correct answer is option 'A'. Can you explain this answer?

Dhruv Mehra answered
Installment for first year = x
Installment for second year = 1.10x
Installment for third year = 1.20x
Installment for third year = 1.30x
Installment for final year = 1.40x
Total amount to be paid = (1 + 1.10 + 1.20 + 1.30 + 1.40) × x = 6450
∴ x = 6450 / 6 = 1075

A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
  • a)
    5%
  • b)
    10%
  • c)
    7%
  • d)
    8%
Correct answer is option 'B'. Can you explain this answer?

Aisha Gupta answered
Let the rate of interest be x% per annum.
For the loan to B:
Simple interest = (5000)(2)(x)/100 = 100x
For the loan to C:
Simple interest = (3000)(4)(x)/100 = 120x
Total simple interest received = 100x + 120x = 220x
Given, 220x = 2200
x = 10
Therefore, the rate of interest per annum is 10%.

A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs. 1 each, interest being simple. The rate of interest charged is:
  • a)
    10%
  • b)
    22%
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?

Pallabi Deshpande answered
Given :
A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs . 1 each interest being simple 
Formula used :
Simple interest = P × R× T /100 
Principal(P), Rate(R) and Time(T)
Calculation :
Let the rate of interest be R% per annum
⇒ Amount to be paid (if paid at the end of 11 months)
⇒ 10 + [10 × R × (11/12) / 100] = 10 + (11R/120)
⇒ Total effective payment = (Rs. 1 + interest on Rs. 1 for 10 months) + (Rs. 1 + interest on Rs. 1 for 9 months) + .... +(Rs. 1 + interest on Rs. 1 for 1 months) + Rs. 1
⇒ (1 + 1 × R × (10/12) / 100)   + (1 + 1 × R × (9/12) / 100) + .... + (1 + 1 × R × (1/12) / 100) + 1
⇒ (1 + 10R/1200) + (1 + 9R/1200) + .... + (1 + R/1200) + 1
⇒ 11 + R(1 + 2 + .... + 10)/1200
⇒ 11 + R(10 × 11 / 2)/1200
⇒ 11 + R(10 × 11 / 2)/1200
⇒ 11 + 11R/240 
Now we have, 
⇒ 10 + 11R/120 = 11 + 11R/240
⇒ 11R/240 = 1
⇒ R = 240/11 = 21× 9/11%
∴ Rate of interest is 21(9/11)%

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum is: 
  • a)
    Rs.600
  • b)
    Rs.645
  • c)
    Rs.525
  • d)
    Rs.625
Correct answer is option 'D'. Can you explain this answer?

Sagar Sharma answered
Given:
- Time period (n) = 2 years
- Rate of interest (r) = 4% per annum
- Difference between compound interest and simple interest = Re. 1

To Find:
The principal sum (P)

Formula:
1. Simple Interest (SI) = P * r * n / 100
2. Compound Interest (CI) = P * (1 + r/100)^n - P

Calculation:
Let's assume the principal sum is P.

Step 1: Calculate Simple Interest (SI):
SI = P * r * n / 100

Step 2: Calculate Compound Interest (CI):
CI = P * (1 + r/100)^n - P

Step 3: Calculate the Difference between CI and SI:
Difference = CI - SI
Re. 1 = P * (1 + r/100)^n - P - P * r * n / 100

Step 4: Substitute the given values:
Re. 1 = P * (1 + 4/100)^2 - P - P * 4 * 2 / 100
Re. 1 = P * (1 + 0.04)^2 - P - P * 0.08

Step 5: Simplify the equation:
Re. 1 = P * (1.04)^2 - P - 0.08P
Re. 1 = P * 1.0816 - P - 0.08P
Re. 1 = 1.0816P - P - 0.08P
Re. 1 = 0.0016P

Step 6: Solve for P:
Re. 1 = 0.0016P
P = Re. 1 / 0.0016
P = Rs. 625

Therefore, the principal sum is Rs. 625. Hence, the correct answer is option D.

Chapter doubts & questions for Simple & Compound Interest - Mathematical Reasoning and Aptitude for UGC NET 2025 is part of UGC NET exam preparation. The chapters have been prepared according to the UGC NET exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for UGC NET 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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