The Miller's are saving up to go on a family vacation in 3 years. They invest \( \$ 2300 \) in an account with an annual interest rate of \( 1.37 \% \). Assuming no withdrawals are made, how much is in the Miller's account after 3 years? Round to the nearest cent. Part 2 of 2 How much interest is earned on the Miller's investment after 3 years? Round to the nearest cent.

We start with an initial deposit (P) of $2,300 and an annual interest rate (r) of 1.37% (written as 0.0137). Since the interest is compounded annually over 3 years (n = 3), the balance (A) is given by the formula:   A = P(1 + r)ⁿ Step 1. Plug in the given numbers:   A = 2300(1 + 0.0137)³     = 2300(1.0137)³ Step 2. Calculate (1.0137)³. A quick way is to use the binomial expansion:   (1.0137)³ = 1 + 3(0.0137) + 3(0.0137)² + (0.0137)³ First, calculate the components:   3(0.0137) = 0.0411   (0.0137)² ≈ 0.00018769, so 3(0.0137)² ≈ 0.00056307   (0.0137)³ ≈ 0.00000257 Now add these to 1:   1 + 0.0411 + 0.00056307 + 0.00000257 ≈ 1.04166564 Step 3. Multiply by the principal:   A ≈ 2300 × 1.04166564   A ≈ 2395.83 Thus, after 3 years the Miller’s account will have approximately $2,395.83. Step 4. To find the interest earned, subtract the principal from the final amount:   Interest = A - P     = 2395.83 - 2300     ≈ $95.83 Final Answers: Part 1: After 3 years, the account holds approximately $2,395.83. Part 2: The interest earned over 3 years is approximately $95.83.