An amount of Rs. 5,000 is invested at a fixed rate of 8% per annum, compounded annually. What will be the value of this investment after 5 years?

Introduction / Context:
This aptitude question tests understanding of compound interest, which is a core concept in time value of money and investment planning. You are given a principal amount, an annual interest rate, a compounding pattern, and a time period, and you must compute the future value of the investment after several years.

Given Data / Assumptions:

• Principal amount P = Rs. 5,000.
• Rate of interest r = 8% per annum.
• Interest is compounded annually.
• Time period n = 5 years.
• No additional deposits or withdrawals during the 5 years.

Concept / Approach:
For compound interest with annual compounding, the amount at the end of n years is given by:
A = P * (1 + r)^n Here r is written in decimal form, so 8% becomes 0.08. The idea is that each year interest is added to the new balance, and then the next year interest is calculated on this increased amount.

Step-by-Step Solution:
Step 1: Convert the rate to decimal form: r = 8% = 0.08. Step 2: Substitute into the formula A = 5000 * (1 + 0.08)^5. Step 3: Compute the growth factor: 1 + 0.08 = 1.08. Step 4: Raise this to the power 5: 1.08^5 ≈ 1.469328. Step 5: Multiply by the principal: A ≈ 5000 * 1.469328 ≈ 7,346.64. Thus, the investment grows to approximately Rs. 7,346.64 after 5 years.

Verification / Alternative Check:
You can verify by compounding year by year. After each year multiply the previous balance by 1.08 and continue for 5 steps. The final figure will again be very close to Rs. 7,346.64, confirming the calculation.

Why Other Options Are Wrong:
Option B (Rs. 6,802.43) is closer to what you get after only 4 years of compounding, not 5 years.
Option C (Rs. 7,934.38) is higher than the correct 5 year value and resembles a value for a higher rate or longer period.
Option D (Rs. 6,381.41) corresponds to a lower interest rate scenario such as 5% per annum, not 8%.
Option E states None of these, which is incorrect because we have a matching correct amount in option A.

Common Pitfalls:
Learners often confuse simple interest with compound interest and may use A = P + P * r * n, which underestimates the true value. Another error is forgetting to convert the percentage to decimal or raising to the wrong power for the number of years.

Final Answer:
The value of the investment after 5 years at 8% per annum compounded annually is Rs. 7,346.64.