Find the principal (in $) that will amount to $25,000 if invested at 3% per annum for 20 years, compounded annually. (You are given the final amount and must find the present value.)

Introduction / Context:
This question is a present value problem under compound interest. We know the future value (amount) after compounding annually, and we must find the initial principal. The compound amount formula is A = P * (1 + r/100)^t. Rearranging gives P = A / (1 + r/100)^t. This is a standard financial math concept: discounting a future amount back to today using the compound growth factor.

Given Data / Assumptions:

• Future amount, A = $25,000
• Annual interest rate, r = 3% per annum
• Time, t = 20 years
• Compounded annually
• Formula: A = P * (1 + r/100)^t

Concept / Approach:
Rearrange compound interest formula to find present value:
P = A / (1 + r/100)^t Here, growth factor = (1.03)^20.

Step-by-Step Solution:
A = 25000 r = 3%, so (1 + r/100) = 1.03 t = 20 P = 25000 / (1.03^20) 1.03^20 ≈ 1.8061 P ≈ 25000 / 1.8061 ≈ 13841.89 Principal ≈ $13,841.89

Verification / Alternative check:
If P ≈ 13841.89, then A = 13841.89 * (1.03^20). Since 1.03^20 ≈ 1.8061, the amount becomes approximately 13841.89*1.8061 ≈ 25000, confirming correctness (small differences occur due to rounding during intermediate steps).

Why Other Options Are Wrong:
$15,625 corresponds to simple interest growth of 60% (1.6 factor), not compounding. $14,821 and $13,468 result from incorrect power/rounding or wrong compounding period. $57,389 is not a present value; it is larger than the future amount, so it cannot be correct.

Common Pitfalls:
Using simple interest instead of compounding, using t = 20 months instead of 20 years, or forgetting to divide by the compound factor and instead multiplying.

Final Answer:
The required principal is approximately $13,841.89.