Question 20 Joey deposits \( \$ 2,500 \) into a savings account. The account pays \( 1.75 \% \) simple interest at an annual rate. How much interest will he earn if he makes no additional deposits or withdrawals for 5 years? What will be the total balance of his account? Interest: \( \$ \square \)

To determine the interest Joey will earn and the total balance in his savings account after 5 years with simple interest, follow these steps: ### 1. **Understand the Simple Interest Formula** The formula for calculating simple interest is: \[ \text{Interest} = P \times r \times t \] Where: - \( P \) = Principal amount (initial deposit) - \( r \) = Annual interest rate (in decimal form) - \( t \) = Time the money is invested (in years) ### 2. **Given Values** - **Principal (\( P \))**: \$2,500 - **Annual Interest Rate (\( r \))**: 1.75\% - **Time (\( t \))**: 5 years ### 3. **Convert Percentage to Decimal** Convert the annual interest rate from a percentage to a decimal: \[ 1.75\% = \frac{1.75}{100} = 0.0175 \] ### 4. **Calculate the Interest Earned** Plug the values into the simple interest formula: \[ \text{Interest} = 2500 \times 0.0175 \times 5 \] \[ \text{Interest} = 2500 \times 0.0875 = \$218.75 \] ### 5. **Determine the Total Balance** Add the interest earned to the principal to find the total balance after 5 years: \[ \text{Total Balance} = \text{Principal} + \text{Interest} = 2500 + 218.75 = \$2,718.75 \] ### **Answer:** - **Interest Earned:** \$218.75 - **Total Balance After 5 Years:** \$2,718.75