What is the rate for getting your paycheck early from a payday lender?

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mathdad
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Although I am currently in the trig sections of my textbook, I decided to also check out questions not involving trigonometry.

You are due a $750 paycheck at the end of the week (Friday), but want to get your hands on the cash on Monday. A payday lender offers to make this deal with you for a fee of 2% of the paycheck. What is the rate you are paying for this service? Assume a 365-day year.

R = rate, B = base , P = percentage given

R = P/B

R = 0.02/750

I do not think this is correct. Forgive my ignorance. This is a silly, easy question.
 
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I = Prt -- Might be a good place to start. You have not specified a method for annualizing the rate.

t = 3/365
r = This is what we seek.
P = 750
I = 750 * 0.02

Go!
 
tkhunny said:
I = Prt -- Might be a good place to start. You have not specified a method for annualizing the rate.

t = 3/365
r = This is what we seek.
P = 750
I = 750 * 0.02

Go!

The options for this question are:

0.5%
18.55
7.14%
182.5%

Which is the answer and how is it done?
 
RTCNTC said:
The options for this question are:

0.5%
18.55
7.14%
182.5%

Which is the answer and how is it done?

Let's start with:

$$I=Prt$$

Solve for $r$:

$$r=\frac{I}{Pt}=\frac{15}{750\cdot\frac{4}{365}}=\frac{73}{40}=\frac{365}{2}\%=182.5\%$$
 
MarkFL said:
Let's start with:

$$I=Prt$$

Solve for $r$:

$$r=\frac{I}{Pt}=\frac{15}{750\cdot\frac{4}{365}}=\frac{73}{40}=\frac{365}{2}\%=182.5\%$$

Another amazing reply.
 
MarkFL said:
Let's start with:

$$I=Prt$$

Solve for $r$:

$$r=\frac{I}{Pt}=\frac{15}{750\cdot\frac{4}{365}}=\frac{73}{40}=\frac{365}{2}\%=182.5\%$$

It is amazing how you went from I = PRT to the answer. Mark, this is what separates a true math guy from a math-guy-wanna-be. I have ZERO idea where the fraction 4/365 came from but I am just a math passionate, middle-aged man hoping to be like you and the rest of the tutors at MHB. A job well-done!
 
RTCNTC said:
It is amazing how you went from I = PRT to the answer. Mark, this is what separates a true math guy from a math-guy-wanna-be. I have ZERO idea where the fraction 4/365 came from but I am just a math passionate, middle-aged man hoping to be like you and the rest of the tutors at MHB. A job well-done!

If you count from Monday to Friday, you find that is a 4 day period, and so this is 4/365 of a year. Since we are finding an APR (annual percentage rate), we want this 4 day period to be expressed in years. If you borrowed some amount of money, and had to pay 2% of it for every 4 days borrowed, you would find that after a year you have paid (2%/(4 days))*(365 days) = 182.5%.
 
Aren't there 5 days from Monday to Friday? Shouldn't the fraction be 5/365.
 
RTCNTC said:
Aren't there 5 days from Monday to Friday? Shouldn't the fraction be 5/365.

How many 24 hour periods are there from noon on Monday, until noon on Friday?
 
RTCNTC said:
Aren't there 5 days from Monday to Friday? Shouldn't the fraction be 5/365.

I went from Friday to Monday (advance 3 days). That's why I managed only 3 days. The correct reading appears to be Monday to Friday (advance 4 days).

You can use Noon each day or beginning-of-day (BOD) or end-of-day (EOD), or virtually anything else. Just be consistent.

Noon Monday to noon Friday is 4 days.
EOD Monday to EOD Friday is 4 days.
BOD Monday to BOD Friday is 4 days.

EOD Monday to BOD Friday is 3 days. That's no good.
BOD Monday to EOD Friday is 5 days. That's no good.

182% is Loan Shark territory.
 
MarkFL said:
How many 24 hour periods are there from noon on Monday, until noon on Friday?

Four. I got it.