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Sagot :
The rule of the monthly payment is
[tex]M\mathrm{}P=\frac{P(\frac{r}{n})}{1-(1+\frac{r}{n})^{-nt}}[/tex]P is the initial amount of the loan
r is the rate in decimal
n is the period per time
t is the time
Let us find the value of them
r = 1.6% = 1.6/100 = 0.016
The interest is compounded monthly, then
n = 12
It is for 6 years, then
t = 6
The monthly payment is $350, Then
M.P = 350
let us substitute these values in the rule above to find P
[tex]350=\frac{P(\frac{0.016}{12})}{1-(1+\frac{0.016}{12})^{-12\times6}}[/tex]We will simplify it
[tex]350=\frac{P(\frac{1}{750})}{1-0.908522108}[/tex][tex]350=\frac{P(\frac{1}{750})}{0.09147789201}[/tex]By using cross multiplication
[tex]350\times0.09147789201=P(\frac{1}{750})[/tex]Multiply both sides by 750 to find P
[tex]P=24012.94665[/tex]a) The Expensive of the care is $24012.94665
The total interest will be the difference between the total monthly payment and the purchase price
The total payment will be the monthly payment multiply by the number of months
[tex]\begin{gathered} A=350\times12\times6 \\ A=25200 \end{gathered}[/tex]The Interset = 25200 - 24012.95 = 1187.05
b) The total interest is $1187.05
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