You have been given the choice to invest $1,200 each year in an account that is expected to pay 3 percent per year or you can invest in an account that pays 4 percent. What is the difference between the returns, if you choose to invest for four years (round to the nearest cent){DO NOT INCLUDE COMMAS OR $}?


We can use the future value of an annuity formula to calculate the returns for both options. The future value of an annuity formula is:

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

Where:
- $ FV $ is the future value (total returns).
- $ P $ is the annual investment ($1,200).
- $ r $ is the annual interest rate (3% = 0.03 or 4% = 0.04).
- $ n $ is the number of years (4 years).

Let's calculate the future value for both accounts and find the difference.

### Step 1: Future value for 3% account
\[
FV_{3\%} = 1200 \times \frac{{(1 + 0.03)^4 - 1}}{0.03}
\]

### Step 2: Future value for 4% account
\[
FV_{4\%} = 1200 \times \frac{{(1 + 0.04)^4 - 1}}{0.04}
\]

### Step 3: Find the difference
\[
\text{{Difference}} = FV_{4\%} - FV_{3\%}
\]

Let me calculate these values for you.The difference between the returns if you invest for four years in the account paying 4% instead of the account paying 3% is **75.40**.

Would you like any more details or have any further questions?

Here are 5 related questions to expand on this:

1. How does the duration of the investment period affect the difference in returns?
2. What would be the difference if the investment period was 10 years instead of 4?
3. How do these returns compare with a higher annual contribution, say $2,000 per year?
4. What if the interest rate was compounded monthly instead of annually?
5. How does the rate of inflation affect the real value of the returns?

**Tip**: The longer the investment period, the greater the impact of the difference in interest rates due to compounding.

You have been given the choice to invest $1,200 each year in an account that is expected to pay 3 percent per year or you can invest in an account that pays 4 percent. What is the difference between the returns, if you choose to invest for four years (round to the nearest cent)?

Explore the difference in returns when investing $1,200 annually for four years in two accounts offering 3% and 4% interest rates. Learn how to calculate future value using the annuity formula and understand the impact of different rates on long-term investments.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation