Question 1178747
Let's break this problem into two parts to find the total amount Joe will have in his account.

**Part 1: First 2 Years of $200 Deposits**

1.  **Monthly Deposit:** $200
2.  **Time Period:** 2 years
3.  **Interest Rate:** 6% per year compounded monthly (0.06 / 12 = 0.005 per month)
4.  **Number of Deposits:** 2 years * 12 months/year = 24 deposits

We'll use the future value of an ordinary annuity formula:

FV = PMT * [((1 + r)^n - 1) / r]

Where:

* FV = Future Value
* PMT = Periodic Payment ($200)
* r = Interest Rate per Period (0.005)
* n = Number of Periods (24)

FV₁ = 200 * [((1 + 0.005)^24 - 1) / 0.005]
FV₁ = 200 * [(1.005^24 - 1) / 0.005]
FV₁ = 200 * [(1.127159776 - 1) / 0.005]
FV₁ = 200 * [0.127159776 / 0.005]
FV₁ = 200 * 25.4319552
FV₁ ≈ $5086.39

**Part 2: Next 3 Years of $300 Deposits**

1.  **Monthly Deposit:** $300
2.  **Time Period:** 3 years
3.  **Interest Rate:** 6% per year compounded monthly (0.06 / 12 = 0.005 per month)
4.  **Number of Deposits:** 3 years * 12 months/year = 36 deposits

We'll use the future value of an ordinary annuity formula again, but we also need to account for the FV₁ amount that has been accruing interest for the entire 5 years.

First calculate the future value of the first 2 years after 5 years.

FV1_5 = FV1 * (1.005)^36
FV1_5 = 5086.39 * (1.005)^36
FV1_5 = 5086.39 * 1.196680526
FV1_5 = $6086.07

Then calculate the future value of the next 3 years.

FV₂ = 300 * [((1 + 0.005)^36 - 1) / 0.005]
FV₂ = 300 * [(1.005^36 - 1) / 0.005]
FV₂ = 300 * [(1.196680526 - 1) / 0.005]
FV₂ = 300 * [0.196680526 / 0.005]
FV₂ = 300 * 39.3361052
FV₂ ≈ $11800.83

**Total Amount in Account:**

* Total = FV1_5 + FV₂
* Total = $6086.07 + $11800.83
* Total = $17886.90

**Answer:**

Joe will have approximately $17,886.90 in his account by the end of 5 years.