Rohan borrowed some money at 10% per annum for first 6 years, 5% per annum for next three years 13% per annum for the period after 9 years. If the interest paid by him at the end of 12 year is Rs 22800, then find how much did he borrowed.

Solution

Let’s denote the amount borrowed by Rohan as \(P\) (the principal amount).

Given:
– Interest rate for the first 6 years: 10% per annum
– Interest rate for the next 3 years: 5% per annum
– Interest rate for the period after 9 years: 13% per annum
– Total interest paid after 12 years: Rs 22800

Step 1: Calculate the interest for each period

– Interest for the first 6 years: \(P \times 10\% \times 6 = 0.6P\)
– Interest for the next 3 years: \(P \times 5\% \times 3 = 0.15P\)
– Interest for the last 3 years: \(P \times 13\% \times 3 = 0.39P\)

Step 2: Calculate the total interest paid

Total interest paid = Interest for the first 6 years + Interest for the next 3 years + Interest for the last 3 years
\[ 22800 = 0.6P + 0.15P + 0.39P \]
\[ 22800 = 1.14P \]

Step 3: Find the principal amount

\[ P = \frac{22800}{1.14} \]
\[ P = 20000 \]

Conclusion

Rohan borrowed Rs 20,000.