SOLUTION: financial planning joe plans to deposit $200 at the end of each month into a bank account for a period of 2 years after which he plans to deposit $300 at the end of each month into

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Question 1178747: financial planning joe plans to deposit $200 at the end of each month into a bank account for a period of 2 years after which he plans to deposit $300 at the end of each month into the same account for another 3 years if the bank pays interest at the rate of 6% per year compounded monthly how much will joe have in his account by the end of 5 years

Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
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.