Quarterly compounding: An investment of ₹1000 earns 10% nominal annual interest compounded quarterly. What is its value at the end of 5 years?

Introduction / Context:
This exercise reinforces how to handle nominal annual rates with sub-annual compounding. When interest is compounded quarterly, the year is divided into four equal periods, each applying one-quarter of the nominal rate. Over multiple years, the total number of compounding periods grows accordingly.

Given Data / Assumptions:

• Principal P = ₹1000.
• Nominal annual interest rate r = 10% = 0.10.
• Quarterly compounding → per-quarter rate i_q = r/4 = 0.025.
• Time T = 5 years → number of quarters n = 5 * 4 = 20.

Concept / Approach:
Use the compound interest formula with sub-annual compounding: F = P * (1 + r/m)^(mT). Here m = 4 (quarters per year). The effective annual rate is (1 + 0.10/4)^4 − 1, but for the full 5-year horizon we directly compute the 20-period growth factor.

Step-by-Step Solution:
Compute per-quarter rate: i_q = 0.10/4 = 0.025.Compute number of periods: n = 20.Apply formula: F = 1000 * (1 + 0.025)^(20).Calculate numeric value: (1.025)^(20) ≈ 1.63862 → F ≈ ₹1,638.62.

Verification / Alternative check:
Check growth annually using the equivalent effective annual rate i_eff = (1.025)^4 − 1 ≈ 0.1038129. Then F = 1000 * (1 + i_eff)^5 ≈ 1000 * (1.1038129)^5 ≈ ₹1,638.62, confirming the calculation.

Why Other Options Are Wrong:
1000 * (1 + 0.10)^(20): Treats 20 years of annual compounding; the period count is wrong.₹1,610: Rough simple-interest style estimate; ignores compounding and underestimates.1000 * (1 + 0.025)^(5): Uses the quarterly rate but only 5 periods instead of 20.₹1,500: A guess that ignores both rate and compounding schedule.

Common Pitfalls:
Mixing nominal and effective rates, using the quarterly rate with an annual period count, or forgetting to multiply years by the number of compounding periods per year.

Final Answer:
₹1,638.62 (i.e., 1000 * (1 + 0.10/4)^(20))