We can solve this problem step by step. Let's break it down using the relevant formulas for compound interest and annuities.

Part 1: How much should the parents save each year to reach $47,000?

We can use the future value of an annuity formula for this:

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

Where:

• $FV = 47,000$ (future value)
• $P$ is the annual payment (what we need to find)
• $r = 7.1\% = 0.071$ (annual interest rate)
• $n = 17$ years

Rearranging the formula to solve for $P$:

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

Let's calculate $P$.

Part 2: How much interest would they earn over the life of the account?

Interest earned is the total future value minus the total contributions:

$\text{Interest} = FV - \text{total contributions}$

Where total contributions are $P \times n$.

Part 3: Determine the value of the fund after 12 years.

For this part, we use the same future value of an annuity formula but with $n = 12$ years.

Part 4: How much interest was earned during the 12th year?

The interest earned during the 12th year is the difference between the value at the end of the 12th year and the value at the end of the 11th year.

Let me calculate everything for you now.### Results:

1. Annual payment: The parents should save $1,510.38 at the end of each year to reach $47,000 after 17 years.

2. Interest earned over the life of the account: They would earn $21,323.55 in interest.

3. Value of the fund after 12 years: After 12 years, the fund will be worth $27,177.89.

4. Interest earned during the 12th year: The interest earned during the 12th year is $3,211.96.

Would you like more details on any of these steps or calculations?

Here are five related questions you might explore next:

1. What happens if the interest rate increases to 8%?
2. How much should they save if they want $60,000 instead of $47,000?
3. How much would they save if the interest was compounded monthly instead of annually?
4. What if they save a lump sum amount initially instead of making annual contributions?
5. How would inflation affect the value of the fund?

Tip: Regularly reviewing savings goals and investment performance can help adjust contributions and stay on track to meet long-term objectives.