gayle has a credit card with $500 balance on it and a 19% interest rate. If she wants to pay off her card in two years, what will her monthly payments be?

i = .19/12 = .0158333

n = 24

500 = x( 1 - 1.01583333^-24)/.01583333
500 = x(19.8378781)
x = 25.20

Well, Gayle is in for a wild ride. Let's calculate her monthly payments and see if they make her break out in laughter or tears.

First, let's convert her interest rate to a decimal. 19% becomes a horrifying 0.19. Yikes!

Next, we need to use the magical formula to calculate the monthly payment:

Payment = (Principal * (Monthly Interest Rate)) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Plugging in Gayle's numbers, we get:

Payment = ($500 * 0.19) / (1 - (1 + 0.19)^(-24))

After doing some math, we find out that Gayle's monthly payment will be approximately $28,631.64!

Oh wait, I made a mistake. Math can be quite slippery at times. Let's try that again.

*recalculating intensifies*

Okay, the real answer is around $25.69. So, Gayle can laugh now, because that monthly payment is actually manageable. Phew!

Just remember, Gayle, don't swipe that credit card carelessly again, or else it'll be me crying, not you!

To calculate Gayle's monthly payments, we need to use the formula for calculating the monthly payment for an amortizing loan. The formula is as follows:

M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:
M = Monthly payment
P = Principal balance (initial amount)
r = Monthly interest rate (annual interest rate / 12)
n = Total number of payments (in months)

First, we need to convert the annual interest rate into a monthly interest rate. In this case, the annual interest rate is 19%, so the monthly interest rate will be 19% / 12, or 0.0167.

Next, we need to determine the total number of payments. Since Gayle wants to pay off her card in two years, she will make 2 * 12 = 24 payments.

Finally, we can calculate the monthly payment using the formula:

M = ($500 * 0.0167 * (1 + 0.0167)^24) / ((1 + 0.0167)^24 - 1)

By simplifying this equation, we can determine Gayle's monthly payments.

To calculate Gayle's monthly payments, we need to consider the principal amount (balance) and the interest rate.

First, let's calculate the interest she will accrue over the two-year period. The interest formula is:

Interest = Principal × Interest Rate × Time

In this case, the principal amount is $500, the interest rate is 19% (or 0.19 as a decimal), and the time is 2 years.

Interest = $500 × 0.19 × 2 = $190

Now, let's add the interest to the principal amount to find the total amount Gayle needs to pay back:

Total amount = Principal + Interest

Total amount = $500 + $190 = $690

Since Gayle wants to pay off her credit card in two years, the total amount can be divided by the number of months in two years (24 months) to find her monthly payment:

Monthly payment = Total amount / Number of months

Monthly payment = $690 / 24 = $28.75 (approx.)

So, Gayle's monthly payments will be approximately $28.75.