) You are planning for a holiday at the end of your course. You require 20 million for spending.
You are planning to invest an amount of money today in a savings account earning 5% interest
compounded annually. How much should you deposit?

To determine how much you should deposit today, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \( A \) is the future amount (20 million),
- \( P \) is the principal (the amount you need to deposit today),
- \( r \) is the annual interest rate (5% or 0.05),
- \( n \) is the number of times the interest is compounded per year (since it's compounded annually, \( n = 1 \)),
- \( t \) is the time in years until the holiday (which is unspecified in this problem, so I’ll denote it as \( t \)).

Rearranging the formula to solve for \( P \):

\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]

Substituting the known values:

\[
P = \frac{20,000,000}{\left(1 + \frac{0.05}{1}\right)^{1 \times t}} = \frac{20,000,000}{(1.05)^t}
\]

Now, to calculate the exact deposit, you'll need to specify the time \( t \) in years. Could you provide that detail?

### Related Questions:
1. What if the interest is compounded monthly instead of annually?
2. How would the deposit change if the interest rate was 7% instead of 5%?
3. How much interest would you earn after a specific time, such as 5 years?
4. What happens if you can make additional monthly contributions to your savings?
5. How would inflation affect the value of your future amount?

### Tip:
The higher the frequency of compounding (e.g., monthly vs annually), the more interest you'll earn over time.

You are planning for a holiday at the end of your course. You require 20 million for spending. You are planning to invest an amount of money today in a savings account earning 5% interest compounded annually. How much should you deposit?

Find out how much you need to deposit today to save 20 million for a future holiday with 5% interest compounded annually. Learn the compound interest formula and how time affects your deposit. Suitable for high school students learning financial math.

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