Ingrid wants to buy a $20,000 car in 8 years. How much money must she deposit at the end quarter paying 5.5% compounded quarterly so that she will have enough to pay for her car?

To determine how much Ingrid must deposit at the end of each quarter to afford the $20,000 car in 8 years, we'll use the formula for the **future value of an ordinary annuity**, which is applicable since the payments are made at the end of each period.

The formula is:

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

Where:
- $FV$ is the future value (the amount Ingrid needs to buy the car, $20,000),
- $P$ is the regular payment (the unknown amount she needs to deposit),
- $r$ is the interest rate per period (quarterly rate),
- $n$ is the total number of periods (total number of quarters in 8 years).

Let's break this down:
- The annual interest rate is 5.5%, so the quarterly interest rate is:
  \[
  r = \frac{5.5\%}{4} = \frac{0.055}{4} = 0.01375
  \]
- The total number of periods

Ingrid wants to buy a $20,000 car in 8 years. How much money must she deposit at the end of each quarter paying 5.5% compounded quarterly so that she will have enough to pay for her car?

Learn how to calculate the quarterly deposits needed for Ingrid to save $20,000 in 8 years at a 5.5% interest rate compounded quarterly. This problem involves key mathematical concepts such as future value of annuities and compound interest, suitable for students in Grades 11-12.

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