Final answer:
Sophia will pay $205.07 in simple interest for a loan of $13,671 at 6% annual rate for 3 months. The total amount she will have to repay is $13,876.07.
Step-by-step explanation:
To calculate the simple interest Sophia will pay for borrowing $13,671 at a 6% annual rate for 3 months, you can use the simple interest formula I = P × r × t, where I is the interest, P is the principal amount, r is the annual interest rate (in decimal form), and t is the time in years.
For Sophia's loan:
- P = $13,671
- r = 6% or 0.06 (as a decimal)
- t = 3 months or 0.25 years (since there are 12 months in a year)
Now, plug these values into the formula:
I = $13,671 × 0.06 × 0.25
I = $205.065
After rounding to the nearest cent, the interest amount is $205.07.
The total amount Sophia will have to pay back at the end of 3 months is the principal plus the interest:
Total Repayment = Principal + Interest
Total Repayment = $13,671 + $205.07
Total Repayment = $13,876.07