Question

Sam is getting ready for a big date when he realizes that he has no money. His roommate, Bill, also has no money, but he has a credit card. Knowing that nobody will let Sam use Bill’s credit card, Sam asks Bill to pull out a cash advance for $120.00. Bill agrees under the condition that Sam is responsible for all interest that accrues on the cash advance which is a 30% interest rate, compounded monthly. The $120 cash advance is repaid in monthly installments over 5 years. How much should Bill ask Sam to pay in interest for the cash advance?

Answer 1

Hi, and welcome to QuestionCove!

When the question says "The $120 cash advance is repaid in monthly installments over 5 years", I assume this means that for each of the 60 months for the next 5 years, 1/60 of the $120, or $2 is repaid?
If that is true, then we can calculate interest based on everything that remains to be repaid. So, each month, we subtract $2 from the amount owed, then add 30%, or multiply by 1.3, and the amount after 60 months is the interest Sam has to pay, I think. Well, I haven't done the calculations yet, but it is not going to turn out well for Sam...

Answer 2

Well, I'm not very handy with equations or calculators, so I wrote a simple script to do the math:
```
remaining = 120
for month in range(1, 61):
remaining = remaining - 2
remaining = remaining *1.3
print("After " + str(month) + "months, " + str(remaining) + " left to pay")
```
And I got the following output (trimmed to the parts we care about):
```
After 1months, 153.4 left to pay
After 2months, 196.82000000000002 left to pay
After 3months, 253.26600000000005 left to pay
...
...
...
After 58months, 452209471.32874364 left to pay
After 59months, 587872310.1273668 left to pay
After 60months, 764234000.5655768 left to pay
```
Wow!
Sam is going to be paying more than 764 million dollars in interest after 5 years if he takes that cash advance, assuming I understood the payment schedule correctly. Compound interest sure is powerful, huh?