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Sagot :
Roderigo will pay $7353.80 in interest.
Interest capitalization means the interest earned is added to the principle amount so first we will use compound interest formula.
What is the formula for compound interest?
[tex]Amount=p(1+\frac{r}{n} )^{nt}[/tex]
p = 8575
r = 7.1% or 0.071
n = 12
t = 4
Putting the values in formula we get
[tex]Amount=8575(1+\frac{0.071}{12} )^{12(4)}[/tex]
[tex]Amount=8575(1+\frac{0.071}{12} )^{48}[/tex]
Solving this we get;
Amount = $11381.94
For the next part we have EMI formula as,
[tex]EMI=\frac{pr(1+r)^{n} }{(1+r)^{n-1}}[/tex]
p = 11381.94
[tex]r=\frac{7.1}{\frac{12}{100} }=0.005917[/tex]
[tex]n=(12)(10)\\n=120[/tex]
[tex]EMI=\frac{11381.94(0.005979)(1+0.005979)^{120} }{(1+0.005979)^{120}-1}[/tex]
EMI = $132.74
Now total payments made in 120 months (10 years) =
[tex]132.74(120)=15928.80[/tex] dollars
interest paid =
[tex]15928.80-8575=7353.80[/tex] dollars
Hence, Roderigo will pay $7353.80
To learn more about the interest visit:
https://brainly.com/question/25793394
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