Simple Interest — Neeta borrows at tiered simple interest: 6% p.a. for the first 3 years, 9% p.a. for the next 5 years, and 13% p.a. for the period beyond 8 years. If the total interest paid in 11 years is ₹ 8160, find the principal borrowed.
Correct Answer: ₹ 8,000
Introduction / Context:When the simple interest rate changes across disjoint periods, total interest equals principal times the sum of periodwise rates * years. The principal can be factored out.
Given Data / Assumptions:
- Years 1–3: 6% p.a.
- Years 4–8: 9% p.a.
- Years 9–11: 13% p.a.
- Total SI over 11 years = ₹ 8160.
Concept / Approach:Let P be principal. Then SI_total = P*(0.06*3 + 0.09*5 + 0.13*3) = P*(0.18 + 0.45 + 0.39) = P*1.02.
Step-by-Step Solution:P * 1.02 = 8160 ⇒ P = 8160 / 1.02 = ₹ 8,000.
Verification / Alternative check:Annualized interest: 6%*3=18%, 9%*5=45%, 13%*3=39%; total 102% of P = ₹ 8160 ⇒ P = 8000.
Why Other Options Are Wrong:₹ 12,000, ₹ 10,000, ₹ 9,000 do not satisfy the 1.02 multiplier.
Common Pitfalls:Confusing percentage points with percent of P; under SI, add (rate * years) linearly.
Final Answer:₹ 8,000