You have $$ \$ 5,000 $$ on a credit card that charges a $$ 18 \% $$ interest rate. If you want to pay off the credit card in 3 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

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We start with the parameters:

- Principal: $$ P = \$5{,}000 $$
- Annual interest rate: $$ r = 18\% $$
- Monthly interest rate: 
  $$
  i = \frac{18\%}{12} = 0.015
  $$
- Total number of months for 3 years: 
  $$
  n = 3 \times 12 = 36
  $$

The formula for the monthly payment $$ M $$ on an installment loan is given by
$$
M = P \cdot \frac{i (1+i)^n}{(1+i)^n - 1}.
$$

Plug in the values:
$$
M = 5000 \cdot \frac{0.015\,(1.015)^{36}}{(1.015)^{36} - 1}.
$$

Next, calculate $$(1.015)^{36}$$. Using the exponential relation,
$$
(1.015)^{36} \approx e^{36 \ln(1.015)}.
$$
Since 
$$
\ln(1.015) \approx 0.014888,
$$
we have 
$$
36 \ln(1.015) \approx 0.536,
$$
and thus,
$$
(1.015)^{36} \approx e^{0.536} \approx 1.709.
$$

Now substitute back into the formula:
$$
M \approx 5000 \cdot \frac{0.015 \times 1.709}{1.709 - 1}.
$$

First, compute the numerator:
$$
0.015 \times 1.709 \approx 0.025635.
$$

Then the denominator:
$$
1.709 - 1 \approx 0.709.
$$

So, the fraction becomes:
$$
\frac{0.025635}{0.709} \approx 0.03617.
$$

Finally, compute the monthly payment:
$$
M \approx 5000 \times 0.03617 \approx 180.88.
$$

Thus, the monthly payment needed is approximately $$\$180.88$$.
You need to pay approximately \$180.88 each month to pay off the \$5,000 credit card balance in 3 years with an 18% interest rate.

You have \( \$ 5,000 \) on a credit card that charges a \( 18 \% \) interest rate. If you want to pay off the credit card in 3 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

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