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An amount of ₹12820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year. The first instalment is 1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interest is 10% per annum, find the
first instalment.?
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An amount of ₹12820 due 3 years hence, is fully repaid in three annual...
Understanding the Problem:
Given:
- Amount due after 3 years: ₹12820
- Repaid in 3 annual instalments starting after 1 year
- First instalment is half the second instalment
- Second instalment is two-thirds of the third instalment
- Rate of interest: 10% per annum

Solution:

Step 1: Finding the Future Value of ₹1 after 3 years
Using the formula for compound interest:
Future Value = Present Value * (1 + Rate)^Time
Future Value of ₹1 after 3 years = 1 * (1 + 0.10)^3
Future Value of ₹1 after 3 years = 1.331

Step 2: Finding the Total Amount Paid after 3 years
Total Amount Paid = 1st instalment + 2nd instalment + 3rd instalment
Let the 2nd instalment be x,
Then, the 1st instalment = x/2 and the 3rd instalment = (3/2)x
Total Amount Paid = x/2 + x + (3/2)x
Total Amount Paid = 4x

Step 3: Calculating the Present Value of the Total Amount Paid
As the total amount is repaid after 3 years, we need to discount it back to the present value using the future value factor we calculated earlier.
Present Value = Total Amount Paid / Future Value of ₹1 after 3 years
Present Value = 4x / 1.331
Given, Present Value = ₹12820
4x / 1.331 = ₹12820
x = ₹4810
Therefore, the first instalment is half of the second instalment, which means the first instalment is ₹2405.
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An amount of ₹12820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year. The first instalment is 1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interest is 10% per annum, find thefirst instalment.?
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An amount of ₹12820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year. The first instalment is 1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interest is 10% per annum, find thefirst instalment.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An amount of ₹12820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year. The first instalment is 1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interest is 10% per annum, find thefirst instalment.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An amount of ₹12820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year. The first instalment is 1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interest is 10% per annum, find thefirst instalment.?.
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