UPSC Exam > UPSC Questions > Kavita got loan of 25000 to purchase a laptop...
Start Learning for Free
Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period?
Most Upvoted Answer
Kavita got loan of 25000 to purchase a laptop if the rate of interest ...
Loan Details
Kavita has taken a loan of ₹25,000 to purchase a laptop. The interest is compounded quarterly at a rate of 12% per annum.
Formula for Compound Interest
To calculate the amount payable after a certain period with compound interest, we use the formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount (initial loan).
- \( r \) = annual interest rate (decimal).
- \( n \) = number of times that interest is compounded per year.
- \( t \) = time the money is invested for in years.
Substituting Values
- \( P = 25000 \)
- \( r = 12\% = 0.12 \)
- \( n = 4 \) (since interest is compounded quarterly)
- \( t = 0.5 \) (for half a year)
Now, substituting these values into the formula:
\[ A = 25000 \left(1 + \frac{0.12}{4}\right)^{4 \times 0.5} \]
Calculating the Amount
1. Calculate \( \frac{r}{n} \):
\( \frac{0.12}{4} = 0.03 \)
2. Calculate \( nt \):
\( 4 \times 0.5 = 2 \)
3. Substitute in the formula:
\( A = 25000 \left(1 + 0.03\right)^{2} \)
\( A = 25000 \left(1.03\right)^{2} \)
\( A = 25000 \times 1.0609 \)
\( A \approx 26522.50 \)
Finding Compound Interest
To find the compound interest (CI), use the formula:
\[ CI = A - P \]
So,
\[ CI = 26522.50 - 25000 \]
\[ CI \approx 1522.50 \]
Final Summary
- **Amount to be paid after half a year:** ₹26,522.50
- **Compound Interest for the period:** ₹1,522.50
Kavita has taken a loan of ₹25,000 to purchase a laptop. The interest is compounded quarterly at a rate of 12% per annum.
Formula for Compound Interest
To calculate the amount payable after a certain period with compound interest, we use the formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount (initial loan).
- \( r \) = annual interest rate (decimal).
- \( n \) = number of times that interest is compounded per year.
- \( t \) = time the money is invested for in years.
Substituting Values
- \( P = 25000 \)
- \( r = 12\% = 0.12 \)
- \( n = 4 \) (since interest is compounded quarterly)
- \( t = 0.5 \) (for half a year)
Now, substituting these values into the formula:
\[ A = 25000 \left(1 + \frac{0.12}{4}\right)^{4 \times 0.5} \]
Calculating the Amount
1. Calculate \( \frac{r}{n} \):
\( \frac{0.12}{4} = 0.03 \)
2. Calculate \( nt \):
\( 4 \times 0.5 = 2 \)
3. Substitute in the formula:
\( A = 25000 \left(1 + 0.03\right)^{2} \)
\( A = 25000 \left(1.03\right)^{2} \)
\( A = 25000 \times 1.0609 \)
\( A \approx 26522.50 \)
Finding Compound Interest
To find the compound interest (CI), use the formula:
\[ CI = A - P \]
So,
\[ CI = 26522.50 - 25000 \]
\[ CI \approx 1522.50 \]
Final Summary
- **Amount to be paid after half a year:** ₹26,522.50
- **Compound Interest for the period:** ₹1,522.50
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period?
Question Description
Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period?.
Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period?.
Solutions for Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period? defined & explained in the simplest way possible. Besides giving the explanation of
Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period?, a detailed solution for Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period? has been provided alongside types of Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period? theory, EduRev gives you an
ample number of questions to practice Kavita got loan of 25000 to purchase a laptop if the rate of interest is 12% pa compounded quarterly find the aMount she pays after half year also find the compound interest for the period? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup