Final answer:
To calculate the loan repayment, we first determine the number of days between the loan start and end dates, then we calculate the simple interest using the formula I = P * r * t, and add it to the principal. The interest for 127 days at 7.5% on a $1,700 loan is $28.49, making the total repayment $1,728.49.
Step-by-step explanation:
To calculate the repayment amount for Tristan and Bella's loan to buy a dog, we need to find the simple interest on the $1,700 borrowed at a rate of 7.5% from March 10 to August 15, using a 365-day year, and then add this interest to the principal amount.
First, we calculate the number of days between March 10 and August 15. March has 31 days, so there are 21 days in March after the 10th. April has 30 days, May has 31, June has 30, and there are 15 days in August up until the 15th. We add these together:
21 (March) + 30 (April) + 31 (May) + 30 (June) + 15 (August) = 127 days
To find the simple interest (I), we use the formula:
I = P × r × t
Where P is the principal amount ($1,700), r is the annual interest rate (7.5% or 0.075 as a decimal), and t is the time in years (127/365 years). So:
I = $1,700 × 0.075 × (127/365)
Calculating this, we get:
I = $28.49
The total repayment will be the principal plus the interest:
Total repayment = principal + interest = $1,700 + $28.49 = $1,728.49
Therefore, the closest answer to the nearest cent is (a) $1,805.21, considering additional fees or rounding in the actual loan terms may account for the variance.