Question

Define this problem Interest $480 principal 4000 rate 3% time 4 years total balance 4480

Answer 1

The problem you've presented involves calculating interest and total balance based on the principal amount, interest rate, and time period. Let's break it down:

1. **Principal (P)**: This is the initial amount of money deposited or borrowed. In this case, it is $4,000.

2. **Interest Rate (r)**: This is the percentage of the principal that is charged as interest for a certain period of time. Here, it is 3% per annum.

3. **Time (t)**: This is the duration for which the money is invested or borrowed, expressed in years. Here, it is 4 years.

4. **Interest (I)**: This is the amount earned (or paid) over time based on the principal and rate. You've stated the interest accumulated is $480.

5. **Total Balance (A)**: This represents the total amount after the interest has been added to the principal. In this case, it is $4,480.

### Calculation

The total balance can be calculated using the formula:

\[
A = P + I
\]

Where:
- \( A \) is the total amount (balance) after time \( t \)
- \( P \) is the principal
- \( I \) is the interest earned

Inserting the given values:

\[
A = 4000 + 480 = 4480
\]

### Verification of Interest

The interest can also be calculated using the formula for simple interest:

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

Where:
- \( r \) is the interest rate expressed as a decimal (3% = 0.03)
- \( t \) is the time in years

Substituting the values:

\[
I = 4000 \times 0.03 \times 4
\]
\[
I = 4000 \times 0.12
\]
\[
I = 480
\]

Both the total balance and the interest calculated confirm the initial problem details.

### Summary

- Principal: $4,000
- Interest Rate: 3%
- Time: 4 years
- Interest Earned: $480
- Total Balance: $4,480

The problem is correctly framed, and the calculations support the values you have provided.