The Bad Guys Co. is notoriously known as a slow-payer. It currently needs to borrow $25,000 and only one company will even deal with Bad Guys. The terms of the loan call for daily payments of $30.76. The first payment is due today. The interest rate is 21% compounded daily. What is the time period of this loan?

Question

Quizplus · Accepted Answer

Using the formula for compound interest:
A = P(1+r/n)^(nt)
where A is the total amount to be paid back, P is the principal amount borrowed, r is the interest rate, n is the number of times compounded per year, and t is the time period in years.

Substituting the given values:
$25,000 = P(1+0.21/365)^(365t)
$25,000 = P(1.00057583)^(365t)
$25,000 = P(1.244499)^t
$25,000 = $30.76 * 365t
t = 2.996 years

Therefore, the time period of this loan is approximately 3.00 years, which corresponds to choice C.