Respuesta :
Annuities
The new home costs $136,000.
2. The down payment is 10%:
DP = 10 * $136,000 / 100 = $13,600
The down payment is $13,600
3. Once he pays the down payment, the amount to borrow is:
$136,000 - $13,600 = $122,400.
He is going to borrow $122,400.
4. Now we need to use the annuities formula for A = $122,400, t = 30 years, r = 3.5%, monthly payments.
The formula is:
[tex]A=R\times\frac{1-\left(1+i\right)^{-n}}{i}[/tex]Where:
R = Amount of the monthly payments
i = Monthly rate of interest
n = Number of payments
Solving for R:
[tex]R=\frac{A\times i}{1-\left(1+i\right)^{-n}}[/tex]Calculate:
[tex]i=\frac{3.5}{100\times12}=0.0029167[/tex]I will keep all the decimals in the calculator. Only a few are shown.
n = 10 years * 12 months per year = 120 payments.
Calculate the amount of the monthly payments:
[tex]\begin{gathered} R=\frac{122,400\times0.002916}{1-\left(1+0.002916\right)^{-120}} \\ Calculating: \\ R=1210.36 \end{gathered}[/tex]The monthly payments would be $1,210.36
5. The final value of the mortgage is given by:
[tex]FV=A\left(1+n\right)^n[/tex]Substituting:
[tex]\begin{gathered} FV=122,400\left(1+0.002916\right)^{120} \\ FV=173,605.41 \end{gathered}[/tex]The interest paid is:
I = FV - A
I = $173,605.41 - $122,400
I = $51,205.41
He would pay $51,205.41 in interest over the lifetime of the mortgage
