Sure, let's solve this step by step.
To find out how much money you owe after 5 years with simple interest, we'll use the simple interest formula:
\(\[ \text{Simple Interest (I)} = \text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)} \]\)
where:
- \(\( P \)\) is the principal amount (initial loan amount)
- \(\( R \)\) is the annual interest rate in decimal form
- \(\( T \)\) is the time period in years
Given:
- \(\( P = 4000 \)\) dollars
- \(\( R = 4.6\% = \frac{4.6}{100} = 0.046 \)\)
- \(\( T = 5 \)\) years
First, let's calculate the simple interest:
\(\[ I = P \times R \times T \]\)
\(\[ I = 4000 \times 0.046 \times 5 \]\)
Now, we calculate step by step:
\(\[ 4000 \times 0.046 = 184 \]\)
\(\[ 184 \times 5 = 920 \]\)
So, the interest \(\( I \)\) accrued over 5 years is \(\( 920 \)\) dollars.
Next, we need to find the total amount owed after 5 years. This is the sum of the principal amount and the interest:
\(\[ \text{Total Amount Owed} = P + I \]\)
\(\[ \text{Total Amount Owed} = 4000 + 920 \]\)
\(\[ \text{Total Amount Owed} = 4920 \]\)
Therefore, after 5 years, you owe \(\( 4920 \)\) dollars.
