Bob wants $35,752 at the end of 6 years in order to buy a car. If his bank pays 4.4% interest, compounded annually, how much must he deposit each year in order to reach his goal?


We are solving for the annual deposit Bob must make to accumulate $35,752 in 6 years, with a 4.4% interest rate compounded annually. This scenario involves a **future value of an ordinary annuity**.

The formula to calculate the future value $FV$ of an ordinary annuity is:

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

Where:
- $FV = 35,752$ (the amount Bob wants at the end of 6 years),
- $P$ is the annual deposit,
- $r = 4.4\% / 100 = 0.044$ (the interest rate per period),
- $n = 6$ (the number of periods).

Now, solving for $P$, the annual deposit:

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

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Here are some questions to expand on this topic:
1. How would the calculation change if the interest rate were compounded monthly instead of annually?
2. What if Bob wanted the car in 8 years instead of 6—how would that affect his annual deposit?
3. How does the interest rate affect the amount of money Bob has to save annually?
4. What would happen if Bob made a lump sum deposit instead of annual deposits?
5. Could Bob achieve his goal faster by increasing his annual deposit?

**Tip**: In problems involving annuities, always remember to account for whether the deposits are made at the start or end of each period!

Bob wants $35,752 at the end of 6 years in order to buy a car. If his bank pays 4.4% interest, compounded annually, how much must he deposit each year in order to reach his goal?

Learn how to calculate the annual deposit Bob must make to accumulate $35,752 in 6 years with a 4.4% interest rate compounded annually. This solution covers the future value of an ordinary annuity formula and key concepts of compound interest, suitable for Grades 10-12.

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