Question

Joel is going to start a business. To cover his start-up costs he takes out two loans. Loan 1: Joel made an initial payment of $2,000 and will make monthly payments of $300 per month. Loan 2: Joel made an initial payment of $1,000 and will make monthly payments of $200 per month. How many months will it take Joel to pay off these two loans if they are $21,500 in total?​

Answer 1

The monthly payments of the loan are illustrations of linear function

It will take Joel 37 months to pay off these two loans if they are $21,500 in total

For the first loan, we have:

• Initial payment: $2000
• Monthly payment: $300

For the second loan, we have:

• Initial payment: $1000
• Monthly payment: $200

So, the monthly payment (y) after each month (x) is:

$y_1 = 2000 + 300x$ --- loan 1

$y_2 = 1000 + 200x$ -- loan 2

Add both equations to get the monthly payment for both loans

$y = y_1 + y_2$

So, we have:

$y = 2000 + 1000 + 300x + 200x$

$y = 3000 + 500x$

The total loan is $21500.

So, we have:

$3000 + 500x = 21500$

Subtract 3000 from both sides

$500x = 18500$

Divide both sides by 500

$x = 37$

Hence, it will take Joel 37 months

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