Suppose you write a program that is supposed to compute the interest
on a bank account at a bank that computes interest on a daily basis, and
suppose you incorrectly write your program so that it computes interest
on an annual basis. What kind of program error is this?

Question

BlackTom AI · Accepted Answer

Choosing annual compounding instead of daily compounding is a textbook example of a logic error: the program runs and produces output but the algorithm/implementation is incorrect.

1) Relevant knowledge points and concepts
- Syntax error: violation of language grammar; program won't compile/run.
- Linker error: unresolved references at link time; program won't link.
- Run-time error: program crashes or throws exceptions during execution.
- Logic (semantic) error: program compiles and runs but produces incorrect results because the implemented logic/algorithm is wrong.
- Compounding formulas: annual compounding A = P(1 + r) for one year; daily compounding A = P(1 + r/365)^{365}.

2) Complete reasoning process step by step
- If the program uses the annual formula but should use the daily formula, it will compile and execute normally because there is no syntax, linker, or runtime fault.
- The output (interest amount) will be numerically incorrect relative to the bank’s daily compounding policy.
- This indicates the problem lies in the program’s logic/algorithm, not in syntax or environment.

3) Calculations with intermediate steps (example)
- Let P = $1000, annual nominal rate r = 0.05 (5%).
- Annual compounding: A_annual = 1000*(1 + 0.05) = 1000*1.05 = $1050.00.
- Daily compounding: r/365 = 0.05/365 ≈ 0.0001369863.
- 1 + r/365 ≈ 1.0001369863. Raise to 365: (1.0001369863)^{365} ≈ e^{0.05} ≈ 1.051271096.
- A_daily ≈ 1000 * 1.051271096 ≈ $1051.27.
- The program using the annual formula would underreport interest by about $1.27 — correct program behavior vs. incorrect logic.

4) Why the correct answer is correct
- The bug is in the choice of formula/algorithm (how interest is computed). Since the program runs but yields wrong numerical results, the error is logical/semantic.

5) Why other options are incorrect
- Syntax Error: would prevent compilation or parsing; not the case here.
- Linker Error: would prevent linking; irrelevant to wrong calculation.
- Run-time Error: would crash or throw exceptions; here the program runs to completion.
- None of the above: incorrect because one of the listed types (Logic Error) correctly describes this bug.

6) Conclusion
The correct classification is Logic Error, which matches the provided answer.

Suppose you write a program that is supposed to compute the interest on a bank account at a bank that computes interest on a daily basis, and suppose you incorrectly write your program so that it computes interest on an annual basis. What kind of program error is this?单项选择题

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