Gene's Art Gallery is notoriously known as a slow-payer.The firm currently needs to borrow $27,500 and only one company will even deal with them.The terms of the loan call for daily payments of $100.The first payment is due today.The interest rate is 24 percent,compounded daily.What is the time period of this loan? Assume a 365 day year.

Question

Quizplus · Accepted Answer

We can use the formula: A = P(1 + r/n)^(nt)
where A = total amount owed, P = principle (original loan amount), r = annual interest rate (24%), n = number of compounding periods per year (365), t = time period in years

Since the loan requires daily payments, n = 365 and t will be in days.
A = 27,500
P = 27,500
r = 0.24
n = 365
Let t be the time period in days.
100 = 27,500(1+0.24/365)^t
1+0.24/365 = 1.0006575
Solving for t:
100/27,500 = (1.0006575)^t
ln(100/27,500) = t ln(1.0006575)
t = ln(100/27,500)/ln(1.0006575)
t ≈ 303.22 days

Therefore, the time period of the loan is 303.22 days.

Gene's Art Gallery Is Notoriously Known as a Slow-Payer