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.

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