Question

A business property is purchased with a promise to pay off a $60,000 loan plus the $16,500 interest by making monthly payments of $1275. The amount of money, y, remaining to be paid on $76500 (the loan plus interest) is reduced by $1275 each month. The amount remaining to be paid can be modeled by the linear function y=76500-1275x where x is the number of monthly payments made. 1. After how many months, will the amount owed equal 0? 2. Will the owner be able to pay off the loan in 4 years?

Answer 1

Part 1

`y=0 \implies 0=76500-1275x\\\\1275x=76500\\\\x=60`

Part 2

No, because 4 years is 48 months, which is less than 60.