Defence Exam > Defence Questions > A sum of Rs. 8400 is taken as loan. This is t...
Start Learning for Free
A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment is
- a)Rs. 4200
- b)Rs. 4480
- c)Rs. 4840
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A sum of Rs. 8400 is taken as loan. This is to be paid in two equal in...
Let the value of each instalment is Rs. z and the principals for 1st and 2nd year are P1 & P2 respectively;
For First year∶
z = P1 (1 + 10/100)
⇒ P1 = 10z/11
For Second year∶
z = P2 (1 + 10/100)2
⇒ P2 = 100z/121
z = P1 (1 + 10/100)
⇒ P1 = 10z/11
For Second year∶
z = P2 (1 + 10/100)2
⇒ P2 = 100z/121
Given that principal is Rs. 8400;
∴ P1 + P2 = 8400;
⇒ 10z/11 + 100z/121 = 8400
⇒ 210z/121 = 8400
⇒ z = 4840
∴ Value of each instalment = Rs. 4840
∴ P1 + P2 = 8400;
⇒ 10z/11 + 100z/121 = 8400
⇒ 210z/121 = 8400
⇒ z = 4840
∴ Value of each instalment = Rs. 4840
Most Upvoted Answer
A sum of Rs. 8400 is taken as loan. This is to be paid in two equal in...
Given:
Principal amount = Rs. 8400
Rate of interest = 10% per annum
Number of instalments = 2
To find: Value of each instalment
Formula:
The formula to calculate the value of each instalment in a loan is given by:
Value of each instalment = Principal amount / Present value of annuity factor
Where,
Present value of annuity factor = (1 - (1 + r)^(-n)) / r
Where,
r = rate of interest per instalment
n = number of instalments
Calculation:
Given that the rate of interest is 10% per annum compounded annually, we need to convert it into the rate of interest per instalment.
Rate of interest per instalment = Rate of interest per annum / Number of instalments
Rate of interest per instalment = 10% / 2 = 5%
Using the formula, we can calculate the present value of annuity factor:
Present value of annuity factor = (1 - (1 + r)^(-n)) / r
Present value of annuity factor = (1 - (1 + 0.05)^(-2)) / 0.05
Present value of annuity factor = (1 - (1.05)^(-2)) / 0.05
Present value of annuity factor = (1 - 1.1025) / 0.05
Present value of annuity factor = (0.1025) / 0.05
Present value of annuity factor = 2.05
Now, we can calculate the value of each instalment:
Value of each instalment = Principal amount / Present value of annuity factor
Value of each instalment = Rs. 8400 / 2.05
Value of each instalment ≈ Rs. 4097.56
Therefore, the value of each instalment is approximately Rs. 4097.56, which is not given in the options. Hence, the correct answer is None of the above.
Principal amount = Rs. 8400
Rate of interest = 10% per annum
Number of instalments = 2
To find: Value of each instalment
Formula:
The formula to calculate the value of each instalment in a loan is given by:
Value of each instalment = Principal amount / Present value of annuity factor
Where,
Present value of annuity factor = (1 - (1 + r)^(-n)) / r
Where,
r = rate of interest per instalment
n = number of instalments
Calculation:
Given that the rate of interest is 10% per annum compounded annually, we need to convert it into the rate of interest per instalment.
Rate of interest per instalment = Rate of interest per annum / Number of instalments
Rate of interest per instalment = 10% / 2 = 5%
Using the formula, we can calculate the present value of annuity factor:
Present value of annuity factor = (1 - (1 + r)^(-n)) / r
Present value of annuity factor = (1 - (1 + 0.05)^(-2)) / 0.05
Present value of annuity factor = (1 - (1.05)^(-2)) / 0.05
Present value of annuity factor = (1 - 1.1025) / 0.05
Present value of annuity factor = (0.1025) / 0.05
Present value of annuity factor = 2.05
Now, we can calculate the value of each instalment:
Value of each instalment = Principal amount / Present value of annuity factor
Value of each instalment = Rs. 8400 / 2.05
Value of each instalment ≈ Rs. 4097.56
Therefore, the value of each instalment is approximately Rs. 4097.56, which is not given in the options. Hence, the correct answer is None of the above.
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
Question Description
A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A sum of Rs. 8400 is taken as loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum compounded annually, then the value of each instalment isa)Rs. 4200b)Rs. 4480c)Rs. 4840d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup