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Q. Some amount was borrowed and paid in two annual installments of ₹ 654 and ₹ 660 respectively. Compound interest charged at 10% per annum. How much was borrowed?
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Q. Some amount was borrowed and paid in two annual installments of ₹ 6...
Given:
- Amount of first installment = ₹ 654
- Amount of second installment = ₹ 660
- Compound interest rate = 10% per annum

To find:
- The amount borrowed

Assumptions:
- The compound interest is charged on the amount borrowed.
- The interest is compounded annually.

Solution:

Let's assume the amount borrowed is 'P'.

Step 1: Calculate the compound interest for the first installment
- The compound interest formula is given by: A = P(1 + r/n)^(nt)
- A is the amount after 't' years
- P is the principal amount (the amount borrowed)
- r is the annual interest rate (10% in this case)
- n is the number of times interest is compounded per year (1 for annual compounding)
- t is the number of years (1 for the first installment)

- We can rearrange the formula to find the principal amount (P):
- P = A / (1 + r/n)^(nt)

- Applying this formula, we have:
- A = ₹ 654
- r = 10% = 0.10
- n = 1
- t = 1

- Substituting the values:
- P = ₹ 654 / (1 + 0.10/1)^(1*1)
- P = ₹ 654 / (1 + 0.10)^1
- P = ₹ 654 / (1.10)^1
- P = ₹ 654 / 1.10
- P ≈ ₹ 594.55

So, the amount borrowed for the first installment is approximately ₹ 594.55.

Step 2: Calculate the compound interest for the second installment
- Using the same formula, we have:
- A = ₹ 660
- r = 10% = 0.10
- n = 1
- t = 1

- Substituting the values:
- P = ₹ 660 / (1 + 0.10/1)^(1*1)
- P = ₹ 660 / (1 + 0.10)^1
- P = ₹ 660 / (1.10)^1
- P = ₹ 660 / 1.10
- P ≈ ₹ 600

So, the amount borrowed for the second installment is approximately ₹ 600.

Step 3: Calculate the total amount borrowed
- The total amount borrowed is the sum of the amounts borrowed for each installment:
- Total amount borrowed = Amount borrowed for first installment + Amount borrowed for second installment
- Total amount borrowed = ₹ 594.55 + ₹ 600
- Total amount borrowed ≈ ₹ 1194.55

Therefore, the amount borrowed is approximately ₹ 1194.55.
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Q. Some amount was borrowed and paid in two annual installments of ₹ 654 and ₹ 660 respectively. Compound interest charged at 10% per annum. How much was borrowed?
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