Celeste Nossiter borrowed $\$ 7500$ from her father to buy a used car. She repaid him after 10 months, at an annual interest rate of $7.7 \%$. Find the total amount she repaid.
The total amount she repaid is $\$$ (Round to the nearest cent as needed.)
Answer
Final Answer: The total amount she repaid is \(\boxed{\$7981.25}\).
Step 1 ：Celeste Nossiter borrowed $7500 from her father to buy a used car. She repaid him after 10 months, at an annual interest rate of 7.7%. We need to find the total amount she repaid.
Step 2 ：The total amount repaid is the principal amount plus the interest. The interest can be calculated using the formula for simple interest which is \(I = PRT\), where \(P\) is the principal amount, \(R\) is the rate of interest, and \(T\) is the time in years.
Step 3 ：In this case, \(P = \$7500\), \(R = 7.7\% = 0.077\) (in decimal form), and \(T = 10/12\) years (since the time is given in months, we need to convert it to years by dividing by 12).
Step 4 ：Substituting the values into the formula, we get \(I = 7500 * 0.077 * 0.8333333333333334\), which simplifies to \(I = \$481.25\).
Step 5 ：The total amount repaid is the sum of the principal and the interest, which is \(\$7500 + \$481.25 = \$7981.25\).
Step 6 ：Final Answer: The total amount she repaid is \(\boxed{\$7981.25}\).
