derek will deposit 1555 per year for 14 years into an account that earns 7%. assuming the first deposit is made 4 years from today how much will be into the account 36 years from today

To solve this, we will break it into two phases: 

1. **Accumulation Phase (Years 4 to 17):** Derek deposits \$1,555 annually for 14 years starting 4 years from today, and each deposit earns 7% interest.
2. **Growth Phase (Years 18 to 36):** After the last deposit is made at the end of year 17, the account continues to grow with no further deposits until year 36.

### Step 1: Determine Future Value of Deposits

We are dealing with an **ordinary annuity**, where payments are made at the end of each period. The future value (FV) of an ordinary annuity can be calculated using the following formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $P = 1,555$ (the annual deposit)
- $r = 0.07$ (the annual interest rate)
- $n = 14$ (the number of years of deposits)

This will give us the value of Derek's account at the end of year 17.

### Step 2: Growth of the Account (Years 18 to 36)

Once the deposits stop after year 17, the money will sit in the account and continue earning 7% interest for the remaining 19 years (from year 18 to 36).

The future value of the amount at the end of year 17 growing without further deposits for the next 19 years can be calculated using the compound interest formula:

\[
FV = P \times (1 + r)^t
\]

Where:
- $P$ is the amount accumulated at the end of year 17,
- $r = 0.07$ is the annual interest rate,
- $t = 19$ years (from year 18 to year 36).

Let's now calculate this step by step. I'll begin by finding the future value of the annuity at the end of year 17.At the end of year 17, the future value of Derek's deposits is \$35,066.01.

### Step 3: Calculate Growth from Year 18 to Year 36

Now, let's calculate how much this amount will grow over the next 19 years (with no additional deposits) at the 7% annual interest rate. We'll use the formula for compound interest:

\[
FV = P \times (1 + r)^{19}
\]

Let me calculate that next.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can guide you through solving the final step manually, or you can ask another question.

Let me know how you'd like to proceed. Here are some questions to consider next:

1. How can I calculate the future value of a lump sum using compound interest?
2. What is the difference between an ordinary annuity and an annuity due?
3. How does compounding frequency affect future value calculations?
4. How can I calculate the present value of an annuity?
5. What is the difference between simple and compound interest?

**Tip:** When solving annuity problems, always separate deposit phases and growth phases to avoid confusion.

Derek will deposit $1,555 per year for 14 years into an account that earns 7%. Assuming the first deposit is made 4 years from today, how much will be in the account 36 years from today?

Calculate the future value of Derek's deposits, where $1,555 is deposited annually for 14 years at a 7% interest rate. Learn the step-by-step process of using the future value of an ordinary annuity formula and the compound interest formula to find the total amount in the account 36 years from today.

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