Respuesta :
Answer:
(-) $29.26 per thousand for a 3-year 3.4% loan
(a) $5,240
(b) $153.32
(c) $279.52
Step-by-step explanation:
• Payment per thousand
The payment amount can be computed from the formula ...
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the principal amount, r is the annual rate, n is the number of payments per year, and t is the number of years.
For a $1000 3-year loan at 3.4%, this evaluates to ...
A = 1000(0.034/12)/(1 -(1 +0.034/12)^(-12·3)) ≈ $29.26
The monthly car payment per $1000 borrowed is $29.26.
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• Rudy's trade-in allowance and down payment will reduce the amount he finances to ...
$10,240 -3000 -2000 = $5,240
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• $5,240 = 5.24 × $1000, so Rudy's payment will be ...
5.24 × $29.26 = $153.32
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• The amount of interest Rudy pays is the difference between the amount paid back and the amount of the loan.
(36 mo)×($153.32/mo) - 5240 = $279.52
Monthly Car Loan Payment Per $1000 Borrowed is $29.26
(a) money he will borrow for loan = $ 5240
(b) monthly auto payment = $ 153.32
(c) the total amount of interest he will pay is $279.52
(d) Total payment for car= $ 10,519.52
Given Information :
- The cost of car is $10,240.
- He has allowance of $3000 and
- He will make a $2000 down payment.
We find out the monthly car loan payment for every $1000 borrowed.
Lets use monthly payment formula
[tex]A=\frac{P\cdot \frac{r}{n} }{1-(1+\frac{r}{n})^{-nt} }[/tex]
Where P is the loan amount.
r is the rate of interest and t is the number of years
n is the period
P=1000
Given that 3-year auto loan at 3.4% APR.
t=3, r= 3.4%= 0.034, n=12
Substitute all the values and calculate the monthly loan
[tex]A=\frac{P\cdot \frac{r}{n} }{1-(1+\frac{r}{n})^{-nt} }\\A=\frac{1000\cdot \frac{0.034}{12} }{1-(1+\frac{0.034}{12})^{-12\cdot 3} }\\A=\frac{1000\cdot \frac{0.034}{12}}{1-\left(\frac{0.034}{12}+1\right)^{-36}}\\A=\frac{2.83333\dots }{1-1.00283\dots ^{-36}}\\A=29.25782[/tex]
Monthly Car Loan Payment Per $1000 Borrowed is $29.26
The cost of car is $10,240. Allowance = 3000 and down payment = 2000
(a) Auto loan = cost of car - allowance - down payment
[tex]Auto \; loan = 10240 - 3000 -2000=5240[/tex]
(b) Monthly Car Loan Payment Per $1000 Borrowed is $29.26
Monthly car loan payment for $5240 is
[tex]\frac{5240}{1000} * 29.26=153.32[/tex]
(c) first we find out the total loan amount paid in 3 years (36 months)
[tex]36 \cdot 153.3224=5,519.52[/tex]
To find the amount of interest he pay , we subtract the loan amount
[tex]5,519.52-5240=279.52[/tex]
the total amount of interest he will pay is $279.52
(d) Total payment for car = down payment +total loan amount paid
Total payment for car =[tex]5000+5519.52=10,519.52[/tex]
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