Aneesh borrowed some money at the rate of 5% per annum for the first 3

Aneesh borrowed some money at the rate of 5% per annum for the first 3 years, 8% per annum for the next 7 years and 12% per annum for the period beyond 10 years. If the total interest paid by him at the end of 13 years is ₹ 5,350, how much money did Aneesh borrow, if the interest is charged as simple interest?

₹ 5,000
₹ 5,500
₹ 5,100
₹ 5,800
This question was previously asked in
UPSC CBI DSP LDCE – 2023
Let the principal amount borrowed be P. The total time period is 13 years. The simple interest rate changes over periods:
Period 1: Rate (R1) = 5% p.a., Time (T1) = 3 years.
Simple Interest for Period 1 (SI1) = (P * R1 * T1) / 100 = (P * 5 * 3) / 100 = 15P / 100.
Period 2: Rate (R2) = 8% p.a., Time (T2) = next 7 years. Total time elapsed = 3 + 7 = 10 years.
Simple Interest for Period 2 (SI2) = (P * R2 * T2) / 100 = (P * 8 * 7) / 100 = 56P / 100.
Period 3: Rate (R3) = 12% p.a., Time (T3) = period beyond 10 years until 13 years. T3 = 13 – 10 = 3 years.
Simple Interest for Period 3 (SI3) = (P * R3 * T3) / 100 = (P * 12 * 3) / 100 = 36P / 100.
The total interest paid is the sum of simple interests for each period.
Total SI = SI1 + SI2 + SI3 = (15P / 100) + (56P / 100) + (36P / 100) = (15P + 56P + 36P) / 100 = 107P / 100.
Given that the total interest paid is ₹ 5,350.
107P / 100 = 5350.
107P = 5350 * 100.
P = (5350 * 100) / 107.
Since 5350 = 107 * 50, we have:
P = (107 * 50 * 100) / 107 = 50 * 100 = ₹ 5,000.
The amount borrowed was ₹ 5,000.
In simple interest, the interest for each period is calculated on the original principal amount. When the rate changes over different periods, the total simple interest is the sum of the interest accumulated during each period with its respective rate and duration.
This method applies specifically to simple interest. For compound interest, the principal would change after each period as accumulated interest is added to the principal.
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