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Answer: Chiara's monthly payment is $194.7
Step-by-step explanation:
The cost of the new natural gas barbecue for $2,100. She made a down payment 30% off the purchase price. This means that the amount of down payment made is
30/100 × 2100 = 0.3 × 2100 = $630
Amount left to pay would be
2100 - 630 = $1470
The formula for determining monthly loan payment is
A = P(r(1 + r)^n)/((1 + r)^n - 1)
There would be 9 monthly payments, so
n = 9
r = 0.055/12 = 0.0046
P = 1470
A = 1470(0.0046(1 + 0.0046)^9)/((1 + 0.0046)^9 - 1)
A = (1470 × 0.0049)/0.037
A = 7.203/0.037
A = 194.67
Chiara's monthly payment when the principal amount is $1470 and the interest rate is 5.5% compounded monthly is $211.44.
What is the formula for the payment amount per period?
The formula for calculating the amount is shown below,
[tex]A =P\dfrac{r(1 + r)^n}{(1 + r)^n - 1}[/tex]
where P is the principal amount, r is the rate of interest per period, and n is the total number of payments or periods.
We know that the cost of the barbecue is $2,100 and Chiara has paid the 30% of the amount, therefore, the remaining balance of the Chiara is 70% of the original cost,
The remaining balance of the Chiara = 70% of $2100
= 0.70 x 2100
= $1470
Now, since Chiara took a loan on the remaining amount of $1470(P) at an interest of 5.5%(r) compounded monthly, and she paid the remaining amount in 9 months(n), therefore, every month installment can be found using the formula,
[tex]A =P\dfrac{r(1 + r)^n}{(1 + r)^n - 1}[/tex]
[tex]A =1470\dfrac{0.055(1 + 0.055)^9}{(1 + 0.055)^9 - 1}\\\\A = \$211.44[/tex]
Hence, Chiara's monthly payment when the principal amount is $1470 and the interest rate is 5.5% compounded monthly is $211.44.
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