Gene's Art Gallery is notoriously known as a slow-payer. The firm currently needs to borrow $27,500 and only one company will deal with them. The terms of the loan call for daily payments of $100. The first payment is due today. The interest rate is 21.9%, compounded daily. What is the time period of this loan? (Assume 365 days in a year)

Question

Gene's Art Gallery is notoriously known as a slow-payer.  The firm currently needs to borrow $27,500 and only one company will deal with them.  The terms of the loan call for daily payments of $100.  The first payment is due today.  The interest rate is 21.9%, compounded daily.  What is the time period of this loan? (Assume 365 days in a year)

Reiny · Answer

assuming payments at the end of the day.

100(1 - 1.0006^-n)/.0006 = 27500
1 - 1.0006^-n = .165
1.006^-n = .835
log both sides and use log rules
-n(log 1.0006) = log .835
-n = -300.6
300 full daily payments of $100 plus a partial payment on the 301st day.