Question

Gerry is buying 80 acres of farmland that cost $250,000. He will take out a 20-year loan with a 1.9% annual interest rate, and he can afford a $1,150 monthly payment.What minimum down payment must Gerry make to keep his monthly payment at or below $1,150?(Answers are rounded to the nearest 10 dollars.)

Answer 1

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:

$A=P(1+\frac{r}{n})^{nt}$

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:

$\begin{gathered} A\text{ = 250000(1 + }\frac{0.019}{12})^{20\times12} \\ \\ A\text{ = \ 365,460} \end{gathered}$

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:

$1150\times20\times12\text{ = \ 276,000}$

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:

$\text{ A = 365,460-276,000 = \ 89,460}$