A payday loan company charges 3.6 percent interest for a four-week period. What would be the annual interest rate from that company?

Note: Assume an even 52 weeks per year. Enter your answer as a percent rounded to 1 decimal place.

BlackTom题目解析

Question

A payday loan company charges 3.6 percent interest for a four-week period. What would be the annual interest rate from that company?

Note: Assume an even 52 weeks per year. Enter your answer as a percent rounded to 1 decimal place.

BlackTom题目解析

BlackTom AI · Accepted Answer

The problem asks to annualize a four-week interest rate of 3.6% assuming a 52-week year. 
First, determine how many four-week periods fit in a year: 52 weeks / 4 weeks = 13 periods per year. 
If each four-week period charges 3.6% interest and we treat it as simple interest per period (no compounding within the year), the annual rate is 3.6% × 13 = 46.8%. 
Common mistakes to watch for: 
- Treating 3.6% as a monthly rate and multiplying by 12 would give 43.2%, which is incorrect here because the period is four weeks, not a calendar month.
- Multiplying the per-period rate by 52 weeks directly (instead of by the number of four-week periods) would yield 187.2%, which misinterprets the period length entirely.
- If one assumed compounding within the year (not specified) the effective annual rate would be higher than 46.8%; for example, (1 + 0.036)^{13} − 1 ≈ 0.585 (58.5%), but the prompt implies a straightforward annualization by period count rather than compound growth.
Thus, using 13 periods per year with 3.6% per period leads to an approximate annual rate of 46.8%, rounded to one decimal place as required.

A payday loan company charges 3.6 percent interest for a four-week period. What would be the annual interest rate from that company? Note: Assume an even 52 weeks per year. Enter your answer as a percent rounded to 1 decimal place. BlackTom题目解析

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