youll be leaving for your study abroad program while there you will need to be able to withdraw the following amounts of money at the end of each respective year. end of year 1: $5000 end of year 2: 10,000 end of year 3: 12000 these amounts of money will be withdrawn from your savings account that pays you a 6% intrest rate every year. how much should you deposit today so that its just enough to make the required future money withdrawls

This problem involves finding the present value of a series of future cash flows. The withdrawals at the end of each year can be seen as future cash flows, and you want to find how much you need to deposit today (the present value) such that, with 6% interest compounding annually, you will be able to make those withdrawals.

The present value formula for each withdrawal can be written as:

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

Where:
- $ PV $ is the present value of the future cash flow,
- $ FV $ is the future value (the amount to be withdrawn),
- $ r $ is the annual interest rate (6% or 0.06),
- $ n $ is the number of years until the cash flow occurs.

We need to calculate the present value for each withdrawal:

### 1. For the withdrawal at the end of year 1 ($5,000):
\[
PV_1 = \frac{5000}{(1 + 0.06)^1} = \frac{5000}{1.06}
\]

### 2. For the withdrawal at the end of year 2 ($10,000):
\[
PV_2 = \frac{10000}{(1 + 0.06)^2} = \frac{10000}{1.06^2}
\]

### 3. For the withdrawal at the end of year 3 ($12,000):
\[
PV_3 = \frac{12000}{(1 + 0.06)^3} = \frac{12000}{1.06^3}
\]

Now, let's calculate these present values and then sum them to find the total amount you should deposit today.To ensure you can make the necessary withdrawals, you should deposit approximately **$23,692.38** today. Here’s the breakdown of the present values for each withdrawal:

1. End of year 1 ($5,000): Present value = $4,716.98
2. End of year 2 ($10,000): Present value = $8,899.96
3. End of year 3 ($12,000): Present value = $10,075.43

Would you like further details, or do you have any questions?

Here are 5 related questions to expand on this topic:
1. What if the interest rate was 8% instead of 6%?
2. How would the required deposit change if the withdrawals were spread over 5 years?
3. How does inflation affect the real value of these withdrawals?
4. What if you made additional deposits each year?
5. Can the same approach be used for continuous compounding?

**Tip:** Understanding present value is key to making sound financial decisions when dealing with future cash flows and investments.

you'll be leaving for your study abroad program. While there, you will need to be able to withdraw the following amounts of money at the end of each respective year: End of year 1: $5,000; End of year 2: $10,000; End of year 3: $12,000. These amounts will be withdrawn from your savings account that pays a 6% interest rate every year. How much should you deposit today so that it is just enough to make the required future withdrawals?

Calculate the present value of future withdrawals ($5,000 at Year 1, $10,000 at Year 2, and $12,000 at Year 3) from a savings account with a 6% interest rate. Learn how to use the present value formula to determine how much to deposit today for financial planning, suitable for Grades 10-12.

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