Question

Find the difference in the balance between simple interest at 5% and compound interest at 6% when $900 is invested for a period of 5 years.(1 point) Responses $1,204.40 $1,204.40 $225 $225 $79.40 $79.40 $304.40

Answer 1

To find the difference in the balance between simple interest and compound interest, we need to calculate both types of interest for the investment amount of $900 over a period of 5 years.

### Step 1: Calculate Simple Interest (SI)

The formula for simple interest is:

\[
SI = P \times r \times t
\]

where:
- \( P = 900 \) (principal)
- \( r = 0.05 \) (interest rate)
- \( t = 5 \) (time in years)

Now, substituting the values:

\[
SI = 900 \times 0.05 \times 5 = 900 \times 0.25 = 225
\]

The total amount with simple interest is:

\[
A_{SI} = P + SI = 900 + 225 = 1125
\]

### Step 2: Calculate Compound Interest (CI)

The formula for compound interest is:

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

where:
- \( P = 900 \) (principal)
- \( r = 0.06 \) (interest rate)
- \( t = 5 \) (time in years)

Now, substituting the values:

\[
A = 900 \times (1 + 0.06)^5 = 900 \times (1.06)^5
\]

Calculating \( (1.06)^5 \):

\[
(1.06)^5 \approx 1.338225
\]

Now, substituting this into the formula:

\[
A \approx 900 \times 1.338225 \approx 1204.4025
\]

Rounding to two decimal places, we get:

\[
A_{CI} \approx 1204.40
\]

### Step 3: Find the Difference

Now, we find the difference between the compound interest amount and the simple interest amount:

\[
\text{Difference} = A_{CI} - A_{SI} = 1204.40 - 1125 = 79.40
\]

### Conclusion

The difference in the balance between simple interest at 5% and compound interest at 6% when $900 is invested for a period of 5 years is:

\[
\boxed{79.40}
\]