Aidan has $3,200 currently saved for a speed boat. If he saves $303 per month and his account earns a 4.3% interest rate, how many years will it take before he can buy the $35,000 boat?

To determine how long it will take Aidan to save enough money to buy a $35,000 speedboat, we need to calculate the time it will take for his savings to grow to that amount, given the following:

- Initial savings: $3,200
- Monthly savings: $303
- Annual interest rate: 4.3%
- Desired amount: $35,000

### Step 1: Convert the Annual Interest Rate to a Monthly Interest Rate
The monthly interest rate $r$ can be calculated by dividing the annual interest rate by 12:

\[
r = \frac{4.3\%}{12} = \frac{0.043}{12} \approx 0.003583
\]

### Step 2: Use the Future Value of an Annuity Formula
The future value of an annuity formula is:

\[
FV = P \times \frac{(1 + r)^n - 1}{r} + P_0 \times (1 + r)^n
\]

Where:
- $FV$ is the future value ($35,000)
- $P$ is the monthly payment ($303)
- $P_0$ is the initial investment ($3,200)
- $r$ is the monthly interest rate (approximately 0.003583)
- $n$ is the number of months (unknown)

We need to solve for $n$, the number of months it will take to reach $35,000.

### Step 3: Solve for $n$ Using Numerical Methods
We'll use numerical methods to find $n$, and then convert it to years.It will take Aidan approximately **7.2 years** to save enough money to buy the $35,000 speedboat.

Would you like more details on this calculation or have any other questions? Here are some related questions you might find interesting:

1. How would increasing his monthly savings impact the time needed to buy the boat?
2. What if the interest rate were higher or lower? How would that change the time needed?
3. How much would Aidan have saved after 5 years at the current savings rate and interest rate?
4. How would a one-time bonus of $5,000 affect the timeline for buying the boat?
5. What if Aidan wanted to buy the boat sooner? How much more would he need to save each month?

**Tip:** Regularly reviewing and adjusting savings goals can help reach them faster, especially when considering changes in income or expenses.

Learn how to calculate the time needed to save enough money to buy a $35,000 speedboat. This problem involves finance concepts including compound interest and the future value of annuities. Suitable for adults interested in financial planning.

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