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

Introduction:
This is a straightforward compound interest calculation. We are told that 5,000 units of money are invested at 8% per annum, compounded annually, and we need to find the amount at the end of 5 years. This tests a standard application of the compound amount formula with annual compounding.

Given Data / Assumptions:

• Principal, P = 5,000 units
• Annual interest rate, r = 8% per annum
• Compounding frequency: annually (once per year)
• Number of years, n = 5 years
• No additional deposits or withdrawals are made during the investment period

Concept / Approach:
For compound interest with annual compounding, the future amount A after n years is: A = P * (1 + r)^n Here r is in decimal form. Since the question asks for the value of the investment after 5 years, we compute A directly using this formula. This includes both the original principal and the accumulated interest.

Step-by-Step Solution:
Step 1: Convert the interest rate from percent to decimal. r = 8% = 0.08 Step 2: Substitute the known values into the compound amount formula. A = 5000 * (1 + 0.08)^5 Step 3: Compute 1 + 0.08. 1 + 0.08 = 1.08 Step 4: Raise 1.08 to the power of 5. 1.08^5 ≈ 1.46933 (rounded) Step 5: Multiply by the principal. A ≈ 5000 * 1.46933 ≈ 7346.64 Step 6: Round to two decimal places. A ≈ 7346.64 units

Verification / Alternative check:
We can also compute year by year to confirm: End of Year 1: 5000 * 1.08 = 5400.00 End of Year 2: 5400 * 1.08 = 5832.00 End of Year 3: 5832 * 1.08 ≈ 6298.56 End of Year 4: 6298.56 * 1.08 ≈ 6802.45 End of Year 5: 6802.45 * 1.08 ≈ 7346.64 This stepwise procedure confirms the computed amount is consistent with the annual compounding process.

Why Other Options Are Wrong:
8346.00: This value is too high and would correspond to a higher rate or a longer investment period than 5 years at 8%. 3456.00: This is below the principal, so it cannot represent a 5 year investment at a positive interest rate. 4567.00: Again, this is less than the principal and not consistent with compounded growth at 8%. 7000.00: Although closer, this still understates the compound growth that occurs at 8% over 5 years. 7346.64: This matches the exact compound interest calculation and is therefore correct.

Common Pitfalls:
Some learners confuse simple and compound interest, incorrectly using A = P(1 + r * n). That would underestimate the amount because it does not include interest on interest. Others might substitute 8 instead of 0.08 for the interest rate or forget to raise the factor to the 5th power. Rounding too early at intermediate steps can also slightly distort the final result, so it is best to keep precision until the final rounding stage.

Final Answer:
The value of the investment after 5 years at 8% per annum compounded annually is 7346.64 units of currency.