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

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) (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.

RELATED QUESTIONS
I'm unable to solve this, please help and many thanks. Lily plans to deposit $8,000 into (answered by solver91311)

4. You are planning to deposit $15,000 into a bank account at the end of each year for 5... (answered by Theo)

1. Lauren plans to deposit $4,000 into a bank account at the beginning of next month and... (answered by ptfile)

you plans to deposit $400 at the end of each year for 2 years, $200 at the end of next... (answered by Theo)

1)Suppose you invest $150 at the end of each month for 6 years into an account earning 6% (answered by ikleyn)

Suppose Mary deposits $200 at the end of each month for 30 years into an account tht pays (answered by Theo)

Please help solving bi,ii Carter expects to live for 30 years more after his retirement. (answered by Theo)

Carter expects to live for 30 years more after his retirement. He would like to withdraw... (answered by asinus)

1.Peter makes equal monthly deposits at the end of each month for the next four years to... (answered by ikleyn)