Franco invested $99,400 in a mutual fund at 4.5% compounded semi-annually. After 2 years, the interest rate was changed to 8.6% compounded quarterly.

a) How much was the value of the fund 6 years after the rate change?

$

b) How much was the total compound interest earned during the whole term?

$

Let's break down the problem step by step:

### Step 1: Initial Investment with 4.5% compounded semi-annually for 2 years

The formula for compound interest is:

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

where:
- $ A $ is the final amount
- $ P $ is the principal (initial investment)
- $ r $ is the annual interest rate (decimal form)
- $ n $ is the number of times interest is compounded per year
- $ t $ is the time the money is invested (in years)

For the first part:
- $ P = 99,400 $
- $ r = 0.045 $
- $ n = 2 $ (since it's compounded semi-annually)
- $ t = 2 $

Let's calculate the value after 2 years at 4.5%.

### Step 2: Calculate the fund's value after 2 years at 4.5%

Once we have the value after 2 years, the interest rate changes to 8.6% compounded quarterly for the next 6 years.

For the second part:
- New $ r = 0.086 $
- New $ n = 4 $ (since it's compounded quarterly)
- $ t = 6 $ (since we are asked about the value 6 years after the rate change)

Now, let's perform the calculations.### a) The value of the fund 6 years after the rate change is approximately **$181,034.17**.

### b) The total compound interest earned during the whole term is approximately **$81,634.17**.

Would you like more details or further clarification?

Here are five related questions you might want to explore:
1. How would the outcome differ if the interest was compounded monthly?
2. What is the impact of continuous compounding on the final amount?
3. How does the length of investment affect the total compound interest earned?
4. What if the interest rate was increased to 10% after the 6-year period?
5. How does changing the compounding frequency affect future value growth?

**Tip:** The more frequent the compounding periods, the greater the total interest earned due to faster reinvestment!

Franco invested $99,400 in a mutual fund at 4.5% compounded semi-annually. After 2 years, the interest rate was changed to 8.6% compounded quarterly. a) How much was the value of the fund 6 years after the rate change? b) How much was the total compound interest earned during the whole term?

Learn how to calculate the value of a mutual fund investment with compound interest. Franco invested $99,400 at 4.5% compounded semi-annually, with the rate changing to 8.6% compounded quarterly. Find out how much the fund is worth after 6 years and the total interest earned.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation