Respuesta :
The annuity formula is given to be:
[tex]PV=PMT\cdot\frac{1-(1+i)^{-n}}{i}[/tex]where
PV = Present Value
PMT = Periodic Payment
i = Interest Rate
n = Number of Periods
If one is to pay 20% down, the loan percentage will be:
[tex]1-0.2=0.8\%[/tex]Therefore, the loan amount will be:
[tex]\Rightarrow0.8\times31567=25253.6[/tex]The interest rate is 6.6%. The monthly rate will therefore be:
[tex]\Rightarrow\frac{6.6}{100\times12}=0.0055[/tex]The number of periods over 14 years is gotten to be:
[tex]\Rightarrow14\times12=168[/tex]Therefore, we have the following parameters to work with:
[tex]\begin{gathered} PV=25253.6 \\ i=0.0055 \\ n=168 \end{gathered}[/tex]To calculate the PMT, we can rewrite the annuity formula to give:
[tex]PMT=\frac{PV\cdot i}{1-(1+i)^{-n}}[/tex]Therefore, we can solve to be:
[tex]\begin{gathered} PMT=\frac{25253.6\times0.0055}{1-(1+0.0055)^{-168}} \\ PMT=230.70 \end{gathered}[/tex]Therefore, the monthly payment is 230.70.
The amount paid is given to be:
[tex]\Rightarrow230.70\times168=38757.6[/tex]Therefore, the interest paid is:
[tex]\Rightarrow38757.6-25253.6=13504[/tex]Therefore, the interest paid is 13,504.
