Assume that your parents wanted to have $ 160 comma 000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 7.0 % per year on their investments. 
a. How much would they have to save each year to reach their​ goal? 

To determine how much your parents need to save each year, we can model this as a **future value of an ordinary annuity** problem, since they are making equal annual payments and the investments earn interest.

The formula for the future value of an ordinary annuity is:

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

Where:
- $FV$ is the future value (the goal, $160,000),
- $P$ is the annual payment (the amount saved each year),
- $r$ is the annual interest rate (7.0%, or 0.07 as a decimal),
- $n$ is the number of payments (17 payments, since they start on the 1st birthday and go until the 17th birthday, which leaves 17 years).

Rearranging the formula to solve for $P$:

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

Now, let's substitute the given values and compute the amount they need to save each year.

\[
P = \frac{160,000 \times 0.07}{(1 + 0.07)^{17} - 1}
\]

I'll calculate this.Your parents would need to save approximately **$5,188.03** each year on your birthday to reach their goal of $160,000 by your 18th birthday, assuming a 7.0% annual return on their investments.

Would you like more details on how the formula works or have any other questions?

Here are some related questions you might find useful:
1. How would the amount change if the interest rate were 5% instead of 7%?
2. What happens if they start saving a year later, i.e., on your 2nd birthday?
3. How would compounding semi-annually instead of annually affect the savings amount?
4. What would happen if they wanted to save $200,000 instead of $160,000?
5. How much total interest would they have earned over the 17 years?

**Tip:** The longer the investment period, the more benefit you get from compound interest, which reduces the annual savings needed.

Assume that your parents wanted to have $160,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 7.0% per year on their investments. How much would they have to save each year to reach their goal?

Determine how much needs to be saved annually to reach a $160,000 college fund by the age of 18, using the future value of an ordinary annuity formula with a 7% annual return. This problem involves financial mathematics concepts such as compound interest.

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