Chiara purchased a new natural gas barbecue for $2,900 and made a down payment that was 30% of the purchase price. She financed the remaining balance for 9 months at an annual interest rate of 5.5% compounded monthly. What is Chiara's monthly payment? (Round your answer to the nearest cent.)
Well, well, well, it's barbecue time! Let's break this down and grill up some numbers.
Chiara's down payment is a staggering 30% of the purchase price. So, 30% of $2,900 gives us $870. That's a lot of hot dogs!
Now, let's calculate the amount she financed. Since she made a down payment of $870, the remaining balance is $2,900 - $870 = $2,030. Not too shabby!
Next up is the interest rate. She'll be paying this off over 9 months, at an annual interest rate of 5.5%, compounded monthly. So, to calculate the monthly interest rate, divide the annual interest rate by 12. In this case, 5.5% / 12 = 0.4583% per month. Let's keep those burgers sizzling!
Now, comes the grand finale – the monthly payment. We can use the formula for calculating the monthly payment on a loan. It goes a little something like this:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^-Number of Months)
Plugging in the values we have, we get:
Monthly Payment = ($2,030 * 0.4583%) / (1 - (1 + 0.4583%)^-9)
Now, let's fire up the calculator and calculate Chiara's monthly payment. Drumroll, please...
After punching in the numbers, we find that Chiara's monthly payment comes out to be approximately $225.42. Voila!
So, to answer your question: Chiara's monthly payment on the natural gas barbecue will be approximately $225.42. It's time to grill, folks!
To calculate Chiara's monthly payment, we need to determine the remaining balance after the down payment and then calculate the monthly payment using the formula for the monthly payment of a loan.
First, let's calculate the down payment:
Down payment = 30% of purchase price
Purchase price = $2,900
Down payment = 30% * $2,900 = $870
Next, let's calculate the remaining balance:
Remaining balance = Purchase price - Down payment = $2,900 - $870 = $2,030
Now, let's calculate the monthly interest rate:
Annual interest rate = 5.5%
Monthly interest rate = (1 + Annual interest rate)^(1/12) - 1
Monthly interest rate = (1 + 0.055)^(1/12) - 1 = 0.004513
Next, let's calculate the number of months:
Number of months = 9
Finally, let's calculate the monthly payment using the formula for the monthly payment of a loan:
Monthly payment = Remaining balance * (Monthly interest rate * (1 + Monthly interest rate)^Number of months) / ((1 + Monthly interest rate)^Number of months - 1)
Monthly payment = $2,030 * (0.004513 * (1 + 0.004513)^9) / ((1 + 0.004513)^9 - 1)
Using a calculator, we can compute the value of the expression, which is approximately $234.25.
Therefore, Chiara's monthly payment for the financed balance is approximately $234.25.