Step-by-step explanation: Cesar, who earned a medical lab technician degree, is currently earning $5000 per month working at a hospital. He has decided to allocate $450 of his monthly earnings towards paying off his student loan debt. If his outstanding loan principal is $34,750, he can use an arithmetic sequence to model the situation.
The formula for finding the nth term of an arithmetic sequence is: an = a1 + (n-1)d, where a represents the nth term, a1 represents the first term, and d represents the common difference. In this case, a1 = 34,750 and d = -450 (negative because he is paying off the loan).
To find out how long it would take for Cesar to pay down the principal of the loan, we need to solve for n when an = 0:
0 = 34,750 - 450(n-1)
n = 78
Therefore, it would take Cesar 78 months, or 6.5 years, to pay down the principal of the loan if he continues to pay $450 every month.
After 36 months, he would have paid off $16,200 ($450 x 36) of the principal, leaving him with $18,550 still owed.
After 72 months, he would have paid off $32,400 ($450 x 72) of the principal, leaving him with $2,350 still owed.