Frederick is saving for a car he is planning to buy in 3 years. He currently does not have any money saved but he has a plan to save $400 each month.

If Frederick puts the money in the piggy bank he keeps on his dresser, how much will he have at the end of 1 year?

4800

How much will he have at the end of  2 years?

9600

How much will he have at the end of 3 years?

14400

If Frederick invests the money with a growth rate of 4.5% annually (compounded monthly), how much will he have at the end of 1 year?

Number

How much will he have at the end of  2 years?

Number

How much will he have at the end of 3 years?

To calculate how much Frederick will have at the end of each year if he invests the money with a growth rate of 4.5% annually, compounded monthly, we need to use the future value of an annuity formula:

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

Where:
- $ FV $ is the future value of the investment.
- $ P $ is the monthly payment ($400).
- $ r $ is the annual interest rate (4.5%, or 0.045).
- $ n $ is the number of times the interest is compounded per year (12 times per year).
- $ t $ is the number of years the money is invested.

Let's calculate the future value for each period (1 year, 2 years, and 3 years).

### 1. At the End of 1 Year:
\[
FV_{1} = 400 \times \left( \frac{(1 + 0.045/12)^{12 \times 1} - 1}{0.045/12} \right)
\]

### 2. At the End of 2 Years:
\[
FV_{2} = 400 \times \left( \frac{(1 + 0.045/12)^{12 \times 2} - 1}{0.045/12} \right)
\]

### 3. At the End of 3 Years:
\[
FV_{3} = 400 \times \left( \frac{(1 + 0.045/12)^{12 \times 3} - 1}{0.045/12} \right)
\]

Let's calculate these values.Here are the amounts Frederick will have at the end of each year if he invests the money with a 4.5% annual growth rate, compounded monthly:

1. **End of 1 year:** $4,900.25
2. **End of 2 years:** $10,025.61
3. **End of 3 years:** $15,386.44

Would you like more details or have any questions?

Here are some related questions to consider:
1. What if the interest rate were different, say 5% instead of 4.5%?
2. How would the total amount change if Frederick increased his monthly savings?
3. What if Frederick decided to invest the money quarterly instead of monthly?
4. How would the future value change if Frederick saved for 4 years instead of 3?
5. What happens if Frederick withdraws part of the money after 2 years?

**Tip:** Regularly reviewing and adjusting your savings plan can help you achieve your financial goals faster.

Learn how to calculate future savings with monthly compounding interest. Frederick plans to save $400 each month for a car in 3 years. Find out how much he will have if he saves in a piggy bank or invests with a 4.5% annual growth rate compounded monthly. Detailed calculations for 1, 2, and 3 years included.

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