Final answer:
The difference between the final account balance for the two loan offers is $275.74, with Offer 2 being the more expensive option due to interest being compounded monthly.
Step-by-step explanation:
To find the difference in the account balances at the end of the loan terms for the two offers, we need to calculate the final amounts for each option and then subtract one from the other.
Offer 1: This is a simple interest loan. The formula to calculate the total amount for a simple interest loan is:
A = P(1 + rt)
However, in this case, we already have the final account balance provided, which is $14,430.
Offer 2: This loan uses compounded interest monthly. The formula for compound interest is:
A = P(1 + −/p)^(nt)
Where:
- P = principal amount ($12,000)
- r = annual interest rate (3.75% or 0.0375)
- n = number of times interest is compounded per year (12)
- t = time the money is invested or borrowed for, in years (66 months / 12 months per year = 5.5 years)
Using these values, we calculate:
A = $12,000(1 + 0.0375/12)^(12*5.5)
A = $12,000(1 + 0.003125)^(66)
A = $12,000(1.003125)^66
A = $12,000*1.2254779
A = $14,705.74
The difference in the total amount at the end of each term is $14,705.74 - $14,430 = $275.74.