You have $$ \$ 4,000 $$ on a credit card that charges a $$ 16 \% $$ interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)? Question Help: Video D Post to forum Submit Question

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UpStudy AI · Accepted Answer

To determine how much you need to pay each month to pay off a credit card balance of $$ \$4,000 $$ at an interest rate of $$ 16\% $$ over $$ 5 $$ years, we can use the formula for the monthly payment on an amortizing loan:

$$
M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}
$$

Where:
- $$ M $$ is the monthly payment
- $$ P $$ is the principal amount (the initial loan balance)
- $$ r $$ is the monthly interest rate (annual interest rate divided by 12)
- $$ n $$ is the number of payments (number of months)

### Step 1: Identify the known values
- $$ P = 4000 $$
- Annual interest rate = $$ 16\% $$ or $$ 0.16 $$
- Monthly interest rate $$ r = \frac{0.16}{12} $$
- Number of years = $$ 5 $$
- Number of months $$ n = 5 \times 12 = 60 $$

### Step 2: Calculate the monthly interest rate
$$
r = \frac{0.16}{12}
$$

### Step 3: Substitute the values into the formula
Now we can substitute $$ P $$, $$ r $$, and $$ n $$ into the formula to find $$ M $$.

Let's calculate $$ r $$ and then $$ M $$.

I'll perform the calculations now.
Calculate the value by following steps:
- step0: Calculate:
  $$5\times 12$$
- step1: Multiply the numbers:
  $$60$$
Calculate or simplify the expression $$ 0.16/12 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.16}{12}$$
- step1: Convert the expressions:
  $$\frac{\frac{4}{25}}{12}$$
- step2: Multiply by the reciprocal:
  $$\frac{4}{25}\times \frac{1}{12}$$
- step3: Reduce the numbers:
  $$\frac{1}{25}\times \frac{1}{3}$$
- step4: Multiply the fractions:
  $$\frac{1}{25\times 3}$$
- step5: Multiply:
  $$\frac{1}{75}$$
Calculate or simplify the expression $$ 4000*(0.0133333333*(1+0.0133333333)^60)/((1+0.0133333333)^60-1) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{4000\left(\frac{133333333}{10000000000}\left(1+\frac{133333333}{10000000000}\right)^{60}\right)}{\left(\left(1+\frac{133333333}{10000000000}\right)^{60}-1\right)}$$
- step1: Remove the parentheses:
  $$\frac{4000\times \frac{133333333}{10000000000}\left(1+\frac{133333333}{10000000000}\right)^{60}}{\left(1+\frac{133333333}{10000000000}\right)^{60}-1}$$
- step2: Add the numbers:
  $$\frac{4000\times \frac{133333333}{10000000000}\left(\frac{10133333333}{10000000000}\right)^{60}}{\left(1+\frac{133333333}{10000000000}\right)^{60}-1}$$
- step3: Add the numbers:
  $$\frac{4000\times \frac{133333333}{10000000000}\left(\frac{10133333333}{10000000000}\right)^{60}}{\left(\frac{10133333333}{10000000000}\right)^{60}-1}$$
- step4: Multiply:
  $$\frac{\frac{133333333\times 10133333333^{60}}{2500000\times 10000000000^{60}}}{\left(\frac{10133333333}{10000000000}\right)^{60}-1}$$
- step5: Subtract the numbers:
  $$\frac{\frac{133333333\times 10133333333^{60}}{2500000\times 10000000000^{60}}}{\frac{10133333333^{60}-10000000000^{60}}{10000000000^{60}}}$$
- step6: Multiply by the reciprocal:
  $$\frac{133333333\times 10133333333^{60}}{2500000\times 10000000000^{60}}\times \frac{10000000000^{60}}{10133333333^{60}-10000000000^{60}}$$
- step7: Rewrite the expression:
  $$\frac{133333333\times 10133333333^{60}}{2500000\times 10000000000^{60}}\times \frac{2500000^{60}\times 4000^{60}}{10133333333^{60}-10000000000^{60}}$$
- step8: Reduce the numbers:
  $$\frac{133333333\times 10133333333^{60}}{10000000000^{60}}\times \frac{2500000^{59}\times 4000^{60}}{10133333333^{60}-10000000000^{60}}$$
- step9: Rewrite the expression:
  $$\frac{133333333\times 10133333333^{60}}{2500000^{60}\times 4000^{60}}\times \frac{2500000^{59}\times 4000^{60}}{10133333333^{60}-10000000000^{60}}$$
- step10: Reduce the numbers:
  $$\frac{133333333\times 10133333333^{60}}{2500000\times 4000^{60}}\times \frac{4000^{60}}{10133333333^{60}-10000000000^{60}}$$
- step11: Rewrite the expression:
  $$\frac{133333333\times 10133333333^{60}}{4000\times 625\times 4000^{60}}\times \frac{4000^{60}}{10133333333^{60}-10000000000^{60}}$$
- step12: Reduce the numbers:
  $$\frac{133333333\times 10133333333^{60}}{625\times 4000^{60}}\times \frac{4000^{59}}{10133333333^{60}-10000000000^{60}}$$
- step13: Rewrite the expression:
  $$\frac{133333333\times 10133333333^{60}}{625\times 4000^{60}}\times \frac{125^{59}\times 32^{59}}{10133333333^{60}-10000000000^{60}}$$
- step14: Rewrite the expression:
  $$\frac{133333333\times 10133333333^{60}}{5^{4}\times 4000^{60}}\times \frac{5^{177}\times 32^{59}}{10133333333^{60}-10000000000^{60}}$$
- step15: Reduce the numbers:
  $$\frac{133333333\times 10133333333^{60}}{4000^{60}}\times \frac{5^{173}\times 32^{59}}{10133333333^{60}-10000000000^{60}}$$
- step16: Rewrite the expression:
  $$\frac{133333333\times 10133333333^{60}}{125^{60}\times 32^{60}}\times \frac{5^{173}\times 32^{59}}{10133333333^{60}-10000000000^{60}}$$
- step17: Rewrite the expression:
  $$\frac{133333333\times 10133333333^{60}}{5^{180}\times 32^{60}}\times \frac{5^{173}\times 32^{59}}{10133333333^{60}-10000000000^{60}}$$
- step18: Reduce the numbers:
  $$\frac{133333333\times 10133333333^{60}}{5^{7}\times 32}\times \frac{1}{10133333333^{60}-10000000000^{60}}$$
- step19: Multiply the fractions:
  $$\frac{133333333\times 10133333333^{60}}{32\times 5^{7}\left(10133333333^{60}-10000000000^{60}\right)}$$
- step20: Multiply:
  $$\frac{133333333\times 10133333333^{60}}{32\times 10133333333^{60}\times 5^{7}-32\times 10000000000^{60}\times 5^{7}}$$
### Step 4: Calculate the monthly payment $$ M $$

We have:
- Monthly interest rate $$ r \approx 0.013333 $$
- Number of months $$ n = 60 $$

Now we can substitute these values into the formula:

$$
M = 4000 \frac{0.013333(1 + 0.013333)^{60}}{(1 + 0.013333)^{60} - 1}
$$

Calculating this gives us:

$$
M \approx 97.27
$$

### Conclusion
To pay off the credit card balance of $$ \$4,000 $$ at a $$ 16\% $$ interest rate over $$ 5 $$ years, you will need to pay approximately $$ \$97.27 $$ each month.
You need to pay approximately \$97.27 each month to pay off the \$4,000 credit card balance at a 16% interest rate over 5 years.

You have \( \$ 4,000 \) on a credit card that charges a \( 16 \% \) interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)? Question Help: Video D Post to forum Submit Question

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