You want to buy a $$ \$ 32,000 $$ car. You can make a $$ 10 \% $$ down payment, and will finance the balance with a $$ 2 \% $$ interest rate for 36 months ( 3 years). What will your monthly payments be?

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To calculate the monthly payments for financing a car, we can use the formula for monthly payments on a loan:

$$ \text{Monthly Payment} = \frac{\text{Loan Amount} \times \text{Interest Rate} \times (1 + \text{Interest Rate})^{Number of Payments}}{(1 + \text{Interest Rate})^{Number of Payments} - 1} $$

Given:
- Loan Amount = $32,000
- Interest Rate = 2% = 0.02
- Number of Payments = 36 months

Substitute the values into the formula to calculate the monthly payment.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{32000\times 0.02\left(1+0.02\right)^{36}}{\left(\left(1+0.02\right)^{36}-1\right)}$$
- step1: Remove the parentheses:
  $$\frac{32000\times 0.02\left(1+0.02\right)^{36}}{\left(1+0.02\right)^{36}-1}$$
- step2: Add the numbers:
  $$\frac{32000\times 0.02\times 1.02^{36}}{\left(1+0.02\right)^{36}-1}$$
- step3: Add the numbers:
  $$\frac{32000\times 0.02\times 1.02^{36}}{1.02^{36}-1}$$
- step4: Convert the expressions:
  $$\frac{32000\times 0.02\left(\frac{51}{50}\right)^{36}}{1.02^{36}-1}$$
- step5: Convert the expressions:
  $$\frac{32000\times 0.02\left(\frac{51}{50}\right)^{36}}{\left(\frac{51}{50}\right)^{36}-1}$$
- step6: Multiply:
  $$\frac{640\times \frac{51^{36}}{50^{36}}}{\left(\frac{51}{50}\right)^{36}-1}$$
- step7: Subtract the numbers:
  $$\frac{640\times \frac{51^{36}}{50^{36}}}{\frac{51^{36}-50^{36}}{50^{36}}}$$
- step8: Evaluate the power:
  $$\frac{\frac{51^{36}}{2^{29}\times 5^{71}}}{\frac{51^{36}-50^{36}}{50^{36}}}$$
- step9: Multiply by the reciprocal:
  $$\frac{51^{36}}{2^{29}\times 5^{71}}\times \frac{50^{36}}{51^{36}-50^{36}}$$
- step10: Rewrite the expression:
  $$\frac{51^{36}}{2^{29}\times 5^{71}}\times \frac{2^{36}\times 25^{36}}{51^{36}-50^{36}}$$
- step11: Reduce the numbers:
  $$\frac{51^{36}}{5^{71}}\times \frac{2^{7}\times 25^{36}}{51^{36}-50^{36}}$$
- step12: Rewrite the expression:
  $$\frac{51^{36}}{5^{71}}\times \frac{2^{7}\times 5^{72}}{51^{36}-50^{36}}$$
- step13: Reduce the numbers:
  $$51^{36}\times \frac{2^{7}\times 5}{51^{36}-50^{36}}$$
- step14: Multiply:
  $$\frac{51^{36}\times 640}{51^{36}-50^{36}}$$
The monthly payment for financing the car will be approximately $1,255.45.
Your monthly payments will be approximately \$1,255.45.

You want to buy a \( \$ 32,000 \) car. You can make a \( 10 \% \) down payment, and will finance the balance with a \( 2 \% \) interest rate for 36 months ( 3 years). What will your monthly payments be?

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