Understanding Interest Practice

To find the difference in interest earnings between a 10% simple interest rate and a 7% compound interest rate after 25 years, we can calculate each separately.

### Step 1: Calculate Simple Interest

The formula for simple interest is given by:

\[
\text{Simple Interest} = P \times r \times t
\]

Where:
- \( P \) is the principal amount (initial investment)
- \( r \) is the rate of interest (as a decimal)
- \( t \) is the time (in years)

For Serenity's investment at 10%:

\[
P = 25000, \quad r = 0.10, \quad t = 25
\]

Substituting the values:

\[
\text{Simple Interest} = 25000 \times 0.10 \times 25 = 25000 \times 2.5 = 62500
\]

So, the total simple interest earned at 10% is **$62,500**.

### Step 2: Calculate Compound Interest

The formula for compound interest is given by:

\[
A = P \times (1 + r)^t
\]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (initial investment)
- \( r \) is the annual interest rate (decimal)
- \( t \) is the number of years the money is invested for

For Serenity's investment at 7%:

\[
P = 25000, \quad r = 0.07, \quad t = 25
\]

Now, calculate the total amount:

\[
A = 25000 \times (1 + 0.07)^{25}
\]

Calculating \( (1 + 0.07)^{25} \):

\[
(1.07)^{25} \approx 5.427
\]

Now, substitute back:

\[
A \approx 25000 \times 5.427 \approx 135675
\]

To find the compound interest earned, we use:

\[
\text{Compound Interest} = A - P = 135675 - 25000 = 110675
\]

So, the total compound interest earned at 7% is **$110,675**.

### Step 3: Calculate the Difference in Interest Earnings

Now we find the difference between the two interest amounts:

\[
\text{Difference} = \text{Compound Interest} - \text{Simple Interest}
\]

Calculating:

\[
\text{Difference} = 110675 - 62500 = 48175
\]

### Final Answer

The difference in interest earnings is **$48,175.00**.