https://file.aiquickdraw.com/mathbot/file/1727922343710igly9d0j.jpg

To solve this problem, we will apply the compound interest formula, as the investment accrues interest semi-annually.

The compound interest formula is:

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

Where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial investment).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

### Given:
- $ P = 4220.80 $
- $ r = 14.45\% = 0.1445 $
- Interest is compounded semi-annually, so $ n = 2 $
- Time period $ t = 4 $ years

Now, let's break this into the two parts of the question:

### a) Total Interest Received:

1. First, calculate the future value $ A $ of the investment using the formula:
   
   \[
   A = 4220.80 \left(1 + \frac{0.1445}{2}\right)^{2 \times 4}
   \]

2. After finding $ A $, the total interest can be calculated as:
   
   \[
   \text{Total Interest} = A - P
   \]

### b) Total Value of the Investment at Maturation:

The total value is simply the future value $ A $, which we will already have calculated in part (a).

Let me calculate this for you.### Calculations:

a) **Total Interest Received**:  
The total interest received at the end of the investment is **$3,154.22**.

b) **Total Value of the Investment at Maturation**:  
The total value of the investment at maturation is **$7,375.02**.

Would you like further clarification on the steps? Here are some related questions:

1. How does compounding frequency affect the total interest earned?
2. What would happen if the interest were compounded annually instead of semi-annually?
3. Can you explain how to convert the percentage rate into decimal form for calculations?
4. What is the difference between simple interest and compound interest?
5. How would the total value change if the investment period were extended?

**Tip**: Always check the compounding frequency in interest problems, as it significantly affects the final amount.

Freda Lynn invested $4220.80 in an investment yielding 14.45% interest SEMI-ANNUALLY for 4 years. Calculate the: a) Total Interest received at the end of the investment. b) Total value of the investment at maturation.

Learn how to calculate the total interest and the value of an investment at maturation with a semi-annual compound interest rate of 14.45% over 4 years. Using the formula A = P(1 + r/n)^(nt), this example explains each step in detail. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation