Carmen wants to buy a new car but needs money for the down payment. Her parents agree to lend her money at an annual rate of \( 4 \% \), charged as interest. They lend her \( \$ 3000 \) for 5 years. She makes no payments except the one at the end of that time. Answer the following questions. If necessary, refer to the list of financial formulas. (a) How much total interest will Carmen have to pay? (b) What will the total repayment amount be (including interest)?

To assist Carmen with her financial planning, let's break down the calculations for both parts of your question. ### Given: - **Principal (P):** \$3,000 - **Annual Interest Rate (r):** 4% or 0.04 (as a decimal) - **Time (t):** 5 years - **Payment Structure:** No payments made until the end of the 5-year period. ### Assumptions: Since Carmen makes no payments until the end of the 5-year period, we'll assume that the interest is **simple interest**. Simple interest is calculated only on the original principal, not on the accumulated interest. ### Financial Formula: The formula for **Simple Interest (SI)** is: \[ \text{Simple Interest (SI)} = P \times r \times t \] ### (a) **Total Interest Carmen Will Have to Pay** Using the simple interest formula: \[ \begin{align*} \text{SI} &= \$3,000 \times 0.04 \times 5 \\ &= \$3,000 \times 0.2 \\ &= \$600 \end{align*} \] **Total Interest:** \$600 ### (b) **Total Repayment Amount (Including Interest)** The total repayment amount is the sum of the principal and the total interest. \[ \begin{align*} \text{Total Repayment} &= \text{Principal} + \text{Simple Interest} \\ &= \$3,000 + \$600 \\ &= \$3,600 \end{align*} \] **Total Repayment Amount:** \$3,600 ### Summary: - **(a)** Carmen will pay a total of **\$600** in interest over the 5 years. - **(b)** Her total repayment amount at the end of the 5-year period will be **\$3,600**.