Final answer:
Sergio's monthly loan payment for the $7,000 home theater equipment, with a 3-year loan term and a fixed annual interest rate of 3.8%, is approximately $205.50 calculated using the loan payment formula.
Step-by-step explanation:
To calculate Sergio's monthly loan payment for his new home theater equipment, we can use the formula for the monthly payment of a fixed-rate loan, which is derived from the annuity formula. The formula is PMT = P * (i / (1 - (1 + i)^(-n))), where:
- P is the principal amount of the loan.
- i is the monthly interest rate.
- n is the total number of payments (number of years times 12, since we want monthly payments).
The principal amount P is $7,000. The annual interest rate is 3.8%, so the monthly interest rate i is 3.8% divided by 12, which is approximately 0.003167. Sergio's loan term is 3 years, so the total number of payments n is 3 times 12, which is 36.
Plugging the values into the formula, we get:
PMT = 7000 * (0.003167 / (1 - (1 + 0.003167)^(-36)))
Solving this, Sergio's monthly loan payment is approximately $205.50.