Respuesta :
Answer:
He has to make a down payment of $89,460
Explanation:
Here, we want to calculate the minimum down payment Gerry must make
Firstly, we need to calculate the total package on the loan
This will include the total amount he has to payback which is the capital plus the interest on the capital
Thus, we need to calculate this amount
Mathematically, we have that as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A is the total amount owed
P is the principal which is the amount borrowed which is $250,000
r is the interest rate which is 1.9% = 1.9/100 = 0.019
T is the time on the loan which is 20 years
n is the number of times per year loan is compounded (since payment will be monthly, this will 12)
We have the amount calculated as:
[tex]\begin{gathered} A\text{ = 250000(1 + }\frac{0.019}{12})^{20\times12} \\ \\ A\text{ = \$365,460} \end{gathered}[/tex]The above has been rounded to the nearest 10 dollars
Now, he can afford a monthly payment of $1,150
If this works, the amount he would have paid at the end of the 20 years will be:
[tex]1150\times20\times12\text{ = \$276,000}[/tex]Now, the minimum downpayment would be the difference between the total sum owed and the sum of all his monthly payments
We have this as:
[tex]\text{ A = 365,460-276,000 = \$89,460}[/tex]