Question 1173174
Let's break down this investment problem step-by-step:

**a) To what sum will the investment grow at the end of 5 years?**

1.  **Identify the variables:**
    * Payment (PMT): $500,000
    * Interest rate per year (r): 12% or 0.12
    * Compounding frequency (n): Quarterly, so 4 times per year
    * Interest rate per period (i): r/n = 0.12 / 4 = 0.03
    * Number of years (t): 5
    * Total number of periods (N): t * n = 5 * 4 = 20

2.  **Use the future value of an ordinary annuity formula:**

    * FV = PMT * [((1 + i)^N - 1) / i]

3.  **Plug in the values:**

    * FV = $500,000 * [((1 + 0.03)^20 - 1) / 0.03]
    * FV = $500,000 * [((1.03)^20 - 1) / 0.03]
    * FV = $500,000 * [(1.80611123467 - 1) / 0.03]
    * FV = $500,000 * [0.80611123467 / 0.03]
    * FV = $500,000 * 26.870374489
    * FV = $13,435,187.24 (approximately)

Therefore, the investment will grow to approximately $13,435,187.24 at the end of 5 years.

**b) How much interest will be earned during this period?**

1.  **Calculate the total amount invested:**
    * Total investment = PMT * N = $500,000 * 20 = $10,000,000

2.  **Calculate the total interest earned:**
    * Total interest = FV - Total investment
    * Total interest = $13,435,187.24 - $10,000,000
    * Total interest = $3,435,187.24

Therefore, the total interest earned during this period will be approximately $3,435,187.24.