New parents wish to save for their newborn's education and wish to have $34,000 at the end of 17 years. How much should the parents place at the end of each year into a savings account that earns an annual rate of 8.7% compounded annually? (Round your answers to two decimal places.)
$ 


How much interest would they earn over the life of the account?
$ 


Determine the value of the fund after 11 years.
$ 


How much interest was earned during the 11th year?

To solve this problem, we can use the formula for the **future value of an ordinary annuity**, which is given by:

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

Where:
- $FV$ is the future value (in this case, $34,000)
- $P$ is the payment made at the end of each year
- $r$ is the annual interest rate (in decimal form, so $8.7\% = 0.087$)
- $n$ is the number of years (in this case, 17)

### Step 1: Determine how much the parents should place at the end of each year

We want to rearrange the formula to solve for $P$:

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

Let’s calculate $P$.

### Step 2: Calculate the total interest earned over the life of the account

The total interest earned is the difference between the future value and the total amount deposited. The total amount deposited is simply the annual payment $P$ multiplied by 17.

### Step 3: Determine the value of the fund after 11 years

To find the value of the fund after 11 years, we use the same formula for the future value of an ordinary annuity, but this time we use $n = 11$.

### Step 4: Find the interest earned during the 11th year

The interest earned during the 11th year is the difference between the value of the fund at the end of the 11th year and the value of the fund at the end of the 10th year.

Let me calculate these for you.

New parents wish to save for their newborn's education and wish to have $34,000 at the end of 17 years. How much should the parents place at the end of each year into a savings account that earns an annual rate of 8.7% compounded annually? (Round your answers to two decimal places.)

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

Determine the value of the fund after 11 years.

How much interest was earned during the 11th year?

Discover how to calculate the annual savings required to reach $34,000 in 17 years with an interest rate of 8.7% compounded annually. Learn how to compute total interest earned, the value of the fund after 11 years, and interest earned during the 11th year.

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