Final answer:
To find the difference in the amount of interest Hannah would have to pay on these two loans, we can calculate the interest for each loan option and then subtract the interest for the 3-year loan from the interest for the 5-year loan. The difference in the amount of interest is $2,340.
Step-by-step explanation:
To find the difference in the amount of interest Hannah would have to pay on these two loans, we need to calculate the interest for each option and then subtract the amount of interest for the 3-year loan from the amount of interest for the 5-year loan.
Calculating the interest for the 3-year loan:
To calculate the interest, we can use the formula: Interest = Principal × Rate × Time. For the 3-year loan, the principal is $12,000, the rate is 6%, and the time is 3 years.
So, the interest for the 3-year loan is:
Interest = $12,000 × 0.06 × 3 = $2,160
Calculating the interest for the 5-year loan:
Using the same formula, for the 5-year loan, the principal is still $12,000, but the rate is 7.5% and the time is 5 years.
So, the interest for the 5-year loan is:
Interest = $12,000 × 0.075 × 5 = $4,500
Calculating the difference:
To find the difference in the amount of interest, we subtract the interest for the 3-year loan from the interest for the 5-year loan:
Difference = $4,500 - $2,160 = $2,340
Therefore, the difference in the amount of interest Hannah would have to pay on these two loans is $2,340.