uppose that you invest $112,300 today. How much will this amount be worth in seven 
years if the interest rate is 7%? How would your answer change if the interest rate is 9%?

This problem involves compound interest. The formula to calculate the future value of an investment under compound interest is:

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

Where:
- $ A $ is the future value of the investment,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times the interest is compounded per year (if it's compounded annually, $ n = 1 $),
- $ t $ is the number of years.

### Case 1: Interest Rate = 7%

For an interest rate of 7%, compounded annually ($ n = 1 $) over 7 years:
\[
A = 112,300 \times \left( 1 + \frac{0.07}{1} \right)^{1 \times 7}
\]
\[
A = 112,300 \times (1.07)^7
\]

### Case 2: Interest Rate = 9%

For an interest rate of 9%, compounded annually ($ n = 1 $) over 7 years:
\[
A = 112,300 \times \left( 1 + \frac{0.09}{1} \right)^{1 \times 7}
\]
\[
A = 112,300 \times (1.09)^7
\]

Let me calculate both results.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can manually calculate the future values using the formulas I provided:

1. For the 7% interest rate:
   \[
   A = 112,300 \times (1.07)^7
   \]
   
2. For the 9% interest rate:
   \[
   A = 112,300 \times (1.09)^7
   \]

Let me know if you need any clarifications or further help with the calculations.

Would you like help with these or further details?

Here are 5 related questions to expand your understanding:
1. What happens if the interest is compounded more frequently (e.g., monthly)?
2. How does the formula change if you make additional yearly investments?
3. How does inflation impact the real value of your investment after 7 years?
4. What if the interest rate changes over the 7-year period?
5. How would the future value differ with simple interest instead of compound interest?

**Tip**: The compound interest formula grows faster when interest is compounded more frequently (e.g., quarterly vs. annually).

Suppose that you invest $112,300 today. How much will this amount be worth in seven years if the interest rate is 7%? How would your answer change if the interest rate is 9%?

Discover how to calculate the future value of a $112,300 investment over seven years with both 7% and 9% interest rates. This guide covers the compound interest formula and explains how to solve the problem step-by-step. Ideal for students and investors looking to understand exponential growth and financial planning.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation