Calculate the future value of an investment of $3000 at 7% annual interest compounded yearly for 5 years.

Introduction / Context:
This question is a direct application of the compound interest formula to find the future value of a single lump-sum investment. It reflects typical situations in savings accounts or fixed deposits where interest is compounded annually at a fixed rate over a specified number of years.

Given Data / Assumptions:

• Principal P = $3000
• Annual interest rate r = 7% per annum
• Time T = 5 years
• Compounding is annual
• We must find the future value (amount) A after 5 years

Concept / Approach:
The standard compound amount formula for annual compounding is:
A = P * (1 + r / 100)^THere, the deposit is made once at the beginning, and interest is added each year on the growing balance. No additional deposits or withdrawals occur during the 5 years.

Step-by-Step Solution:
Step 1: Substitute the given values in the formula.A = 3000 * (1 + 7 / 100)^5Step 2: Simplify the rate term.1 + 7 / 100 = 1.07Step 3: Compute (1.07)^5.(1.07)^2 ≈ 1.1449(1.07)^3 ≈ 1.2250(1.07)^4 ≈ 1.3108(1.07)^5 ≈ 1.40255 (more precisely 1.4025517)Step 4: Multiply by the principal.A ≈ 3000 * 1.4025517 ≈ $4207.66

Verification / Alternative check:
You can verify using a financial calculator or spreadsheet function such as FV. Setting rate = 0.07, nper = 5, pmt = 0, pv = -3000 will return a future value close to 4207.66, confirming the calculation. Any small difference comes only from rounding intermediate steps.

Why Other Options Are Wrong:
$5207 and $5687: These assume either a much higher interest rate or a longer time period.$4376: Slightly higher than the correct value, likely from miscalculating (1.07)^5.$4000: Too low; it corresponds roughly to a lower effective interest rate.

Common Pitfalls:
Students sometimes apply simple interest instead of compound interest, or confuse the number of years. Another common error is to round early when computing powers, leading to noticeable errors in the final amount. Keep more decimal places in intermediate calculations and round only at the end.

Final Answer:
The future value of $3000 invested at 7% per annum compounded annually for 5 years is approximately $4207.66.