If you had a loan for $30,000 at an annual interest rate of 8 percent with a 90-day interest prepayment penalty, what would be the amount of your penalty?

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BlackTom AI · Accepted Answer

We start by restating the problem: a loan of $30,000 with an annual interest rate of 8% and a 90-day interest prepayment penalty. We need to compute the penalty amount.

Option 1: $400. To test this, calculate 90 days of interest on $30,000. If a 360-day year is assumed (common in finance), the daily rate is 8%/360 = 0.022222...% per day, and the 90-day interest would be 30,000 × 0.08 × (90/360) = 30,000 × 0.02 = $600. $400 would imply using a much smaller period or rate, which is inconsistent with the stated 8% annual rate for a 90-day window.

Option 2: $200. This would correspond to roughly 90 days of interest at a much lower rate, or a calculation mistake such as using 30 days or dividing by 365 and rounding aggressively. It does not align with the standard 360-day year convention for loan penalties and the given principal.

Option 3: $2400. This would equal the full-year interest on $30,000 (30,000 × 0.08 = 2,400) and would ignore the 90-day restriction entirely. A 90-day penalty is typically a fraction of annual interest, not the entire yearly amount, so this overstates the charge.

Option 4: $600. This matches the conventional 360-day-year approach: penalty = principal × annual rate × (days in penalty / 360) = 30,000 × 0.08 × (90/360) = 30,000 × 0.02 = $600. This aligns with standard loan practice for a 90-day period expressed as a fraction of a year.

In summary, the incorrect options fail because they either understate or overstate the implied 90-day interest when applying the 8% annual rate and the typical 360-day year convention. The $600 calculation properly scales the annual rate to a 90-day window using the common 360-day year basis, producing the expected penalty amount.

Introduction to Personal Finance CP - 2 - Beatty - Preparatory Academy - 1st Semester - 2025/2026 Unit 3: Exam- Requires Respondus LockDown Browser

If you had a loan for $30,000 at an annual interest rate of 8 percent with a 90-day interest prepayment penalty, what would be the amount of your penalty?

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