The Ayoub's family would like to borrow $60,000 to purchase a home. They qualified for an annual interest rate of 4.8%. Algebraically determine the fewest number of whole years the Ayoub's family would need to include in the mortgage agreement in order to have a monthly payment of no more than $720.

In this question, we have a family seeking to finance their house project by getting a loan at a rate of 4.8% per annum. We now need to know the number of possible years that the family would have to include in the mortgage agreement so that they won’t pay more than $720 per month.

Firstly let’s have a parallel unit of time. If they are paying $720 per month, this means per year, the amount to be paid would be $8,640 per year. Let’s say the total number of years in which they would be repaying the loan would be t years; this means the total amount they would be repaying is $8,640t

Now we know that this total amount is indicative of the principal amount borrowed plus the interest paid annually for a number of t years.

Mathematically, what we have is that;

$8,640t = $60,000 + interest

Let’s have an expression for the interest!

The interest can be figured in terms of simple interest.

I = PRT/100

in this question, P = $60,000

R = rate = 4.8%

T = t years

On substitution;

I = (60,000 * 4.8 * t)/100 = $2,880t

Now, let’s put this back into that $8640t equation;

$8,640t = $60,000 + interest

$8,640t = $60,000 + $2,880t

$8640t - $2880t = $60,000

5,760t = 60,000

t = 60,000/5,760 = 10.41 years

This is closest to 10 years