The amount which should be invested at 4.5% per annum simple interest, if you require $15 700 in three years’ time, is closest to:

Question

BlackTom AI · Accepted Answer

Simple interest formula A = P(1 + rt), so to find the principal P we rearrange to P = A / (1 + rt).

Relevant concepts:
- Simple interest grows linearly with time: interest = P * r * t.
- Total accumulated amount after t years: A = P + interest = P(1 + rt).
- Here A = 15,700, r = 4.5% = 0.045 (per year), t = 3 years.

Step-by-step calculation:
1. Compute the simple-interest factor: 1 + r t = 1 + 0.045 × 3.
   0.045 × 3 = 0.135, so 1 + r t = 1.135.
2. Solve for P: P = A / (1 + r t) = 15,700 / 1.135.
3. Divide: 15,700 ÷ 1.135 = 15,700 × (1 / 1.135).
   Note 1 / 1.135 = 200/227 ≈ 0.881057269.
   Multiply: 15,700 × 0.881057269 ≈ 13,832.602.
4. Round to cents: $13,832.60.

Why this is correct:
- Substituting P = $13,832.60 back gives interest = P × r × t = 13,832.60 × 0.045 × 3 = 1,867.40. Adding principal + interest yields 13,832.60 + 1,867.40 = 15,700, which matches the required future amount. Thus the principal computed is consistent with the simple interest model.

Why the other options are incorrect:
- (a) $1,867.40 is the total interest earned over 3 years (not the required principal).
- (b) $13,757.86 is close because it likely assumes compound interest (A = P(1 + r)^t) rather than simple interest; it does not satisfy the simple interest equation.
- (c) $13,720.80 is further from the correct simple-interest result and likely stems from arithmetic or formula errors.

Conclusion: The correct present amount to invest under simple interest is $13,832.60, matching option d.

The amount which should be invested at 4.5% per annum simple interest, if you require $15 700 in three years’ time, is closest to:单项选择题

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