Questions: A = 650(1+0.04)^30

Transcript text: $A=\$ 650(1+0.04)^{30}$

Solution

Solution Steps

To solve the given expression for $ A $, we need to calculate the future value of an investment using the formula for compound interest. The formula is $ A = P(1 + r)^n $, where $ P $ is the principal amount, $ r $ is the annual interest rate, and $ n $ is the number of years. Here, $ P = 650 $, $ r = 0.04 $, and $ n = 30 $.

Step 1: Identify the Variables

We are given the principal amount $ P = 650 $, the annual interest rate $ r = 0.04 $, and the number of years $ n = 30 $.

Step 2: Apply the Compound Interest Formula

We use the formula for compound interest: \[ A = P(1 + r)^n \] Substituting the values: \[ A = 650(1 + 0.04)^{30} \]

Step 3: Calculate the Future Value

Calculating $ (1 + 0.04)^{30} $: \[ (1 + 0.04)^{30} \approx 3.2434 \] Now, substituting back into the equation: \[ A \approx 650 \times 3.2434 \approx 2108.2084 \]

Final Answer

Thus, the future value $ A $ is approximately: \[ \boxed{A \approx 2108.2084} \]

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