CP will need save some money to open a new branch of convenient store in 3 years. A special account, which yields 2% compounded quarterly, is prepared for CP to set aside $18000 at the end of every 3-month period, to accumulate the money.

How much money will CP have after 3 years? $Answer


This is a problem involving compound interest with regular contributions. The formula used for future value in such a case (with periodic contributions and compound interest) is:

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

Where:
- $FV$ is the future value.
- $P$ is the regular contribution (in this case, $18,000).
- $i$ is the interest rate per period (compounded quarterly, so we divide the annual rate by 4).
- $n$ is the total number of periods (quarterly contributions for 3 years means 12 periods).

Given:
- The annual interest rate is 2%, so $i = \frac{0.02}{4} = 0.005$.
- $P = 18,000$ (the contribution made at the end of every 3 months).
- $n = 4 \times 3 = 12$ (the total number of quarterly periods over 3 years).

Now, let's calculate the future value.After 3 years, CP will have approximately **$222,040.12** in the account.

Do you want more details or have any questions about the process? 

Here are 5 related questions to explore this topic further:
1. How would the final amount change if the interest were compounded monthly instead of quarterly?
2. What if the interest rate increased to 3%? How would the future value be affected?
3. How much would CP need to contribute each quarter to reach $250,000 in 3 years?
4. Can we calculate the interest earned after 3 years?
5. How does the time period affect the future value in compound interest scenarios?

**Tip**: Always remember that more frequent compounding periods (like monthly or weekly) result in more interest earned over time.

CP will need to save some money to open a new branch of a convenience store in 3 years. A special account, which yields 2% compounded quarterly, is prepared for CP to set aside $18,000 at the end of every 3-month period, to accumulate the money. How much money will CP have after 3 years?

Learn how to calculate the future value of CP's account after 3 years of quarterly contributions of $18,000, with a 2% interest rate compounded quarterly. This problem demonstrates the compound interest formula for periodic payments. Suitable for high school students studying finance and compound interest.

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