Bad Guys plc 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?(Assume 365 days in a year.)

Question

Quizplus · Accepted Answer

The time period of the loan can be calculated using the formula for the present value of an annuity due, since the first payment is made immediately. The formula is $PV = P \times \frac{1 - (1 + r)^{-n}}{r}$, where $PV$ is the present value (loan amount), $P$ is the payment amount, $r$ is the daily interest rate, and $n$ is the total number of payments. Rearranging the formula to solve for $n$, and substituting $PV = £25,000$, $P = £30.76$, and $r = \frac{21\%}{365} = 0.000575342$, we can solve for $n$. The calculation gives $n \approx 1095$ days, which is approximately 3 years when divided by 365.

Bad Guys Plc Is Notoriously Known as a Slow-Payer