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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 compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is: 
  • a)
    Rs. 500
  • b)
    Rs. 400
  • c)
    Rs. 450
  • d)
    Rs. 600
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Given data:
Compound Interest = Rs. 525
Rate of Interest = 10%
Time = 2 years

To find:
Simple Interest for double the time at half the rate of interest

Solution:
Let the principal amount be P.

Using the formula for compound interest, we have:

P(1 + 10/100)^2 - P = 525

Simplifying the above equation, we get:

P = 4500

Now, we need to find the simple interest for double the time at half the rate of interest.

New time = 4 years (double the time)
New rate of interest = 5% (half of 10%)

Using the formula for simple interest, we have:

SI = (P * R * T) / 100
SI = (4500 * 5 * 4) / 100
SI = Rs. 900

Therefore, the simple interest for double the time at half the rate of interest is Rs. 900, which is not one of the given options. However, we need to note that the question is asking for the simple interest on the same sum, which means we need to use the same principal amount of Rs. 4500.

If we calculate the simple interest for 2 years at 5%, we get:

SI = (4500 * 5 * 2) / 100
SI = Rs. 450

Hence, the correct answer is option A, Rs. 500.

What is the rate of simple interest for the first 4 years if the sum of Rs. 360 becomes Rs. 540 in 9 years and the rate of interest for the last 5 years is 6%?
  • a)
    4%    
  • b)
    5%
  • c)
    3%    
  • d)
    6%
Correct answer is option 'B'. Can you explain this answer?

Pranjal Choudhury answered
For the last 5 years, the interest earned would be: 30% of 360 = 108. Thus, interest earned in the first 4 years would be Rs. 72 → Rs. 18 every year on an amount of Rs. 360- which means that the rate of interest is 5%

What is the simple interest for 9 years on a sum of Rs. 800 if the rate of interest for the first 4 years is 8% per annum and for the last 4 years is 6% per annum?
  • a)
    400
  • b)
    392
  • c)
    352
  • d)
    Cannot be determined
Correct answer is option 'D'. Can you explain this answer?

Pallabi Kumar answered
8% of 800 for 4 years + 6% of 800 for 4 years = 64 x 4 + 48 x 4 = 256 + 192 = 448. However, we do not know the rate of interest applicable in the 5 th year and hence cannot determine the exact simple interest for 9 years.

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)%

If the difference between the simple interest and compound interest on some principal amount at 20% per annum for 3 years is Rs. 48, then the principle amount must be
  • a)
    Rs. 550
  • b)
    Rs. 500
  • c)
    Rs. 375
  • d)
    Rs. 400
Correct answer is option 'C'. Can you explain this answer?

Aman Chatterjee answered
Solve using options. If we try 500 (option b) for convenience, we can see that the difference between the two is Rs. 64 (as the SI would amount to 300 and Cl would amount to 100 + 120 + 144 = 364). Since, we need a difference of only Rs. 48 we can realize that the value should be 3/4th of 500. Hence, 375 is correct.

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

Divide Rs. 3903 between Amar and Akbar such that Amar’s share at the end of 7 years is equal to Akbar’s share at the end of 9 years at 4% p.a. rate of compound interest.
  • a)
    Amar = Rs. 2028, Akbar = Rs. 1875
  • b)
    Amar = Rs. 2008, Akbar = Rs. 1000
  • c)
    Amar = Rs. 2902, Akbar = Rs. 1001
  • d)
    Amar = Rs. 2600, Akbar = Rs. 1303
Correct answer is option 'A'. Can you explain this answer?

Dhruv Mehra answered
Akbars’ share should be such that at 4% p.a. compound interest it should become equal to Amar’s share in 2 years. Checking thorugh the options it is clear that option (a) fits perfectly as 1875 would become 2028 in 2 years @4% p.a. compound interest.

If a certain sum of money becomes double at simple interest in 12 years, what would be the rate of interest per annum?
  • a)
    8.33
  • b)
    10
  • c)
    12
  • d)
    14
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Given information:
- Sum of money becomes double at simple interest in 12 years

To find:
- Rate of interest per annum

Solution:
Let the principal be P.
After 12 years, the amount becomes 2P.
Since the interest is simple interest, the interest earned each year is the same.
Let the rate of interest per annum be R%.

Therefore, the interest earned in 12 years = P * R% * 12

According to the given information, the amount after 12 years = P + P * R% * 12 = 2P

Simplifying, we get:
P(1 + 12R/100) = 2P
1 + 12R/100 = 2
12R/100 = 1
R = 8.33%

Therefore, the rate of interest per annum is 8.33%.

Answer: Option A) 8.33

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%

Find the principal if compound interest is charged on the principal at the rate of 16 2/3 % per annum for two years and the sum becomes Rs. 196.
  • a)
    Rs. 140
  • b)
    Rs. 154
  • c)
    Rs. 150
  • d)
    Rs. 144
Correct answer is option 'D'. Can you explain this answer?

Anand Goyal answered
Let's solve this step by step:
Understanding the problem:
  • We need to find the principal amount.
  • The rate of interest is 16 2/3% per annum, which is equivalent to 50/3%.
  • The time period is 2 years.
  • The final amount (principal + interest) is Rs. 196.
Formula for compound interest:
  • Amount (A) = Principal (P) * (1 + Rate/100)^Time
Substituting the values:
  • 196 = P * (1 + 50/300)^2
  • 196 = P * (7/6)^2
  • 196 = P * 49/36
Solving for Principal (P):
  • P = 196 * 36 / 49
  • P = 144
Therefore, the principal amount is Rs. 144.
So, the correct answer is option 4: Rs. 144.

A sum of Rs. 600 amounts to Rs. 720 in 4 years at Simple Interest. What will it amount to if the rate of interest is increased by 2%?
  • a)
    Rs. 648
  • b)
    Rs. 768
  • c)
    Rs. 726
  • d)
    Rs. 792
Correct answer is option 'B'. Can you explain this answer?

Alok Kapoor answered
600 becomes 720 in 4 years SI —> SI per year = Rs. 30 and hence the SI rate is 5%.
At 7% rate of interest the value of 600 would become 768 in 4 years. (600 + 28% of 600)

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