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Bruce is considering purchasing a car for $10,000. He is thinking about using his savings to make a [tex]$20 \%$[/tex] down payment and then financing the difference over a 4-year loan.

If he doesn't make the down payment, he'll qualify for an interest rate of [tex]$8.0 \%[tex]$[/tex].
If he makes the down payment, he'll qualify for an interest rate of [tex]$[/tex]7.0 \%$[/tex].

Use the amortization table provided to complete the statement. Round to the nearest cent, if necessary.

Making the down payment will lower Bruce's monthly car payment by $\square$ a month.


Sagot :

Let's solve for how much making the down payment will lower Bruce's monthly car payment.

1. Car Price and Down Payment Calculation:
- The car's total price is [tex]$510,000. - A 20% down payment on the car price amounts to $[/tex]102,000.

2. Loan Amount with Down Payment:
- When Bruce makes the down payment, the remaining amount to be financed is:
[tex]\[ 510,000 - 102,000 = 408,000 \][/tex]

3. Loan Amount without Down Payment:
- If Bruce doesn't make the down payment, the entire car price will be financed:
[tex]\[ 510,000 \][/tex]

4. Interest Rates:
- With the down payment, the annual interest rate is 7.0%, which translates to a monthly interest rate:
[tex]\[ \frac{7.0\%}{12} = \frac{0.07}{12} \approx 0.005833 \, (\text{monthly interest rate}) \][/tex]
- Without the down payment, the annual interest rate is 8.0%, translating to a monthly interest rate:
[tex]\[ \frac{8.0\%}{12} = \frac{0.08}{12} \approx 0.006667 \, (\text{monthly interest rate}) \][/tex]

5. Loan Term:
- The loan term is 4 years, which is [tex]\(4 \times 12 = 48\)[/tex] months.

6. Monthly Payments:
- Monthly payment with the down payment is calculated to be approximately [tex]$9770.07. - Monthly payment without the down payment is calculated to be approximately $[/tex]12450.59.

7. Difference in Monthly Payments:
- The difference between the two monthly payments is:
[tex]\[ 12450.59 - 9770.07 = 2680.52 \][/tex]

Making the down payment will lower Bruce's monthly car payment by $2680.52.

Thus, Bruce's monthly car payment will be lowered by [tex]\(\boxed{2680.52}\)[/tex] dollars.
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