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