Equal annual instalments — Aptitude Question
Equal annual instalments: A sum of ₹1,000 is to be repaid in two equal annual instalments at 5% simple interest on… Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 150 seconds
Question
A sum of ₹1,000 is to be repaid in two equal annual instalments at 5% simple interest on the outstanding amount. What is each instalment, to the nearest rupee?
Options
- ₹525
- ₹537
- ₹550
- ₹564
Show the answer and the worked solution
Correct answer: B. ₹537
Worked solution
- Under simple interest the present value of a payment after n years is x/(1 + 0.05n).
- x/1.05 + x/1.10 = 1,000.
- x(0.95238 + 0.90909) = 1,000 → x × 1.86147 = 1,000.
- x ≈ ₹537.
Answer: ₹537.
The idea
Bring every instalment back to its present value and set the total equal to the sum borrowed. Note that simple interest discounts by dividing by (1 + rn), not by a power.
Shortcut. Carry everything to the end of year 2: ₹1,000 grows to ₹1,100, while the first instalment earns a year's 5%, so 2.05x = 1,100 and x ≈ ₹537.
Common trap. ₹550 — splitting the ₹1,100 owed after two years into equal halves, forgetting that the first payment, made a year early, clears part of the debt and earns its own 5%.
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