Find rate from present worth: At simple interest, the present worth of $1245 due in 15 months is $1200. What is the annual rate of interest?
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A3%
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B4%
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C6%
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D5%
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E2.5%
Answer
Correct Answer: 3%
Explanation
Introduction / Context:The link between present worth P, future sum S, time t in years, and annual simple-interest rate r is S = P * (1 + r t). Knowing P, S, and t, we can directly solve for r as a simple proportion, then express it per annum as a percentage.
Given Data / Assumptions:
- S = $1245 (due amount).
- P = $1200 (present worth).
- t = 15 months = 1.25 years.
Concept / Approach:Use S = P(1 + r t) ⇒ r = (S/P − 1) / t. Substitute numerical values, being careful to convert months to years, and finally multiply by 100 to get percent per annum.
Step-by-Step Solution:
S/P − 1 = 1245/1200 − 1 = 0.0375.t = 1.25 years.r = 0.0375 / 1.25 = 0.03 = 3% per annum.Verification / Alternative check:Check forward: P(1 + r t) = 1200 * (1 + 0.03 * 1.25) = 1200 * 1.0375 = 1245, consistent.
Why Other Options Are Wrong:
- 4%, 5%, 6%: Do not satisfy the proportional relation at 1.25 years.
Common Pitfalls:Forgetting to convert months to years or mixing the bases (using discount formulas instead of simple-interest growth).
Final Answer:3%