CP will need $290000 to open a new branch of convenient store in 3 years. A special account, which yields 5% compounded quarterly, is prepared for CP to set aside equal amounts, every 3-month period, to accumulate the required money.
How much money should CP save every 3 months?

This problem involves calculating the regular payments into a compound interest account, which is a classic application of the **future value of an annuity formula**.

The formula for the future value of an ordinary annuity is:

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

Where:
- $ FV $ is the future value (the amount CP wants to accumulate, which is $290,000),
- $ P $ is the payment made every period (this is what we need to find),
- $ 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 quarterly, $ n = 4 $),
- $ t $ is the number of years (3 years).

### Step 1: Substitute known values
- $ FV = 290,000 $
- $ r = 0.05 $
- $ n = 4 $
- $ t = 3 $

\[
290,000 = P \times \left( \frac{(1 + 0.05/4)^{4 \times 3} - 1}{0.05/4} \right)
\]

### Step 2: Solve for $ P $
I'll compute this equation step by step.The amount that CP should save every 3 months is approximately **$22,549.91**.

Would you like further details on the calculation or have any questions?

Here are 5 related questions that could deepen your understanding:
1. How would the required savings change if the interest rate were higher or lower?
2. What if CP needed the $290,000 in 5 years instead of 3 years?
3. How does the frequency of compounding (monthly vs quarterly) affect the savings needed?
4. How would a one-time lump sum deposit differ from making regular payments?
5. What happens if CP skips a payment—how will that impact the total savings?

**Tip:** Regular contributions into a compound interest account grow faster due to interest compounding, so saving consistently is key to reaching financial goals.

CP will need $290000 to open a new branch of convenient store in 3 years. A special account, which yields 5% compounded quarterly, is prepared for CP to set aside equal amounts, every 3-month period, to accumulate the required money. How much money should CP save every 3 months?

Discover how to calculate the regular savings needed to accumulate $290,000 in 3 years with 5% quarterly compounded interest. Using the future value of annuity formula, find out how much CP needs to save every 3 months to reach their financial goal.

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