Question

​Let's assume that a carpenter borrowed ​$2 comma 000 to be paid off in a year to finance a machine that would make him work faster. As a​ result, he is able to take on more projects and collect ​$400 more earnings in the first​ year, after paying off the principal of ​$2 comma 000. ​However, there is a 15​% rental fee​ (interest) on his loan that he also has to pay off. The carpenter earned an extra ​$ nothing in the first year.

Answer 1

The carpenter earned an extra $100.

Step-by-step explanation:

Since this problem deals with a one-year loan with an yearly interest rate, it can be treated as a simple interest problem. For simple interests, the final value (Vf) can be found by multiplying the initial value (Vi) by one plus the interest rate (i) as shown below:

`V_(f)= V_(i)*(1+i)\\V_(f)=2,000*(1+0,15)\\V_(f)=2,300`

To find how much extra money the carpenter made in the first year, one should subtract the final value of loan from the $2,000 dollars down payment plus the extra $400 he collected for the year

`Earnings = 2,000+400-2,300 = 100`.

Therefore, the carpenter earned an extra $100.