The Art Gallery is notoriously known as a slow-payer. The firm currently needs to borrow $25,000 and only one company will loan to them. The terms of the loan call for weekly payments of $500 at a weekly interest rate of .45%. What is the loan term?

Question

Quizplus · Accepted Answer

To find the loan term, we can use the formula:

Loan amount = (Weekly payment) x [(1 - (1 + Weekly interest rate)^(-Number of weeks)) / Weekly interest rate]

Substituting the given values, we have:

$25,000 = $500 x [(1 - (1 + 0.0045)^(-Number of weeks)) / 0.0045]

Simplifying and solving for the number of weeks, we get:

Number of weeks = - [ln(1 - 25000 x 0.0045 / 500) / ln(1 + 0.0045)] ≈ 56.77

Therefore, the loan term is approximately 56.77 weeks, which is closest to choice C (56.77 weeks).

The Art Gallery Is Notoriously Known as a Slow-Payer