Answer:
Roderigo will pay $7353.80 in interest.
Step-by-step explanation:
Interest capitalization means the interest earned is added to the principle amount so first we will use compound interest formula.
Compound interest formula is :
[tex]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]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]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1 }[/tex]
p = 11381.94
r = [tex]7.1/12/100=0.005917[/tex]
n = [tex]12\times10=120[/tex]
[tex]\frac{11381.94\times0.005917\times(1+0.0059147)^{120} }{(1+0.005917)^{120}-1 }[/tex]
= [tex]\frac{11381.94\times0.005917\times(1.005917)^{120} }{(1.005917)^{120}-1 }[/tex]
EMI = $132.74
Now total payments made in 120 months (10 years) = [tex]132.74\times120=15928.80[/tex] dollars
Now, interest paid = [tex]15928.80-8575=7353.80[/tex] dollars
Hence, Roderigo will pay $7353.80 in interest.
