If you save $2500 today and you want to have $4000 in 4 years, what interest rate do you need to earn?

Assume annual compounding.  Round to one decimal place.  



To solve this, we can use the future value formula for compound interest:

\[
FV = PV \times (1 + r)^n
\]

Where:
- $ FV $ is the future value, which is $4000.
- $ PV $ is the present value or initial amount, which is $2500.
- $ r $ is the annual interest rate we are solving for.
- $ n $ is the number of years, which is 4.

### Step 1: Set up the equation with the values

\[
4000 = 2500 \times (1 + r)^4
\]

### Step 2: Isolate $ (1 + r)^4 $

\[
\frac{4000}{2500} = (1 + r)^4
\]

\[
1.6 = (1 + r)^4
\]

### Step 3: Take the fourth root of both sides

To solve for $ r $, take the fourth root of 1.6.

\[
1 + r = \sqrt[4]{1.6}
\]

Using a calculator for the fourth root of 1.6:

\[
1 + r \approx 1.1253
\]

### Step 4: Solve for $ r $

\[
r \approx 1.1253 - 1
\]

\[
r \approx 0.1253
\]

Converting to a percentage and rounding to one decimal place:

\[
r \approx 12.5\%
\]

### Answer
You would need to earn an interest rate of approximately **12.5%** per year.

Would you like more details or have any questions?

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Here are 5 questions that build on this:
1. How would the required interest rate change if you wanted $5000 instead of $4000 in 4 years?
2. What would the required interest rate be if the compounding was monthly instead of annually?
3. How much would you have in 4 years with a fixed interest rate of 10%?
4. If you saved $3000 instead of $2500, what interest rate would you need for $4000 in 4 years?
5. How long would it take to reach $4000 at a fixed rate of 10%?

**Tip:** When interest is compounded more frequently than annually, the effective interest rate is slightly higher.

If you save $2500 today and you want to have $4000 in 4 years, what interest rate do you need to earn? Assume annual compounding. Round to one decimal place.

Discover how to calculate the interest rate needed to grow a $2500 investment to $4000 over 4 years with annual compounding. This solution includes key steps in applying the compound interest formula and solving for the rate, suitable for high school math students.

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