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?

The correct answer is 56.77 weeks.

Explanation:

According to the scenario, the given data are as follows:

PV = $25,000

Payment (pmt) = $500

Rate of interest (r) =.45% per week

Time period (t) = ?

So, we can calculate the loan term period by using following formula:

PV : Pmt = (1 - (1 + r) ^ - t) : r

So, by putting the value we get,

$25,000 : $500 = (1 - (1 + 0.0045) ^-n) : 0.0045

$50 = (1 - (1 + 0.0045) ^-n) : 0.0045

$50 * 0.0045 = (1 - (1 + 0.0045) ^-t)

0.225 = (1 - (1 + 0.0045) ^-t)

(1 + 0.0045) ^-t) = 1 - 0.225

((1.0045) ^-t) = 0.775

t = 56.77

Hence, the loan term period is 56.77 weeks.