Answer:
a. $58.57
Explanation:
Billy is in a pickle. He has a credit card debt of $3500 with a 16% annual interest rate, and he wants to pay it off in a year. He also wants to ask his boss for a raise, but he doesn't know how much to ask for. Luckily, he has a friend who is good at math and can help him out.
The friend tells Billy that we need to use the formula for the monthly payment of a credit card debt, which is:
P = (r / 12) * B / (1 - (1 + r / 12)^(-n))
where P is the monthly payment, r is the annual interest rate, B is the current balance, and n is the number of months to pay off the debt.
Using this formula, the friend calculates how much Billy is currently paying and how much he would need to pay to clear his debt in 12 months. The friend also finds the difference between these two payments, which is the amount of extra income Billy would need from his raise.
The friend shows Billy the calculations and says:
"Here you go, Billy. You are currently paying $280.42 per month to pay off your debt in 15 months. If you want to pay it off in 12 months, you would need to pay $331.79 per month. That means you would need an additional monthly income of $51.37 from your raise. The closest answer choice to this amount is a. $58.57, so this is the best option."
Billy thanks his friend and says:
"Wow, you are amazing! Thank you so much for helping me out. I'm going to ask my boss for a raise right now. Wish me luck!"
The friend wishes Billy good luck and hopes that he will get his raise and pay off his debt soon.