To determine the principal amount (P) that will amount to $5525 at a simple interest over 3 years, we need to use the simple interest formula. The formula for the total amount (A) accumulated through simple interest is:
[tex]\[ A = P(1 + RT) \][/tex]
where:
- [tex]\( A \)[/tex] is the total amount after time [tex]\( T \)[/tex]
- [tex]\( P \)[/tex] is the principal amount (initial sum of money)
- [tex]\( R \)[/tex] is the rate of interest per unit time (as a decimal or fraction)
- [tex]\( T \)[/tex] is the time the money is invested or borrowed for (in years)
In this specific problem:
[tex]\[ A = 5525 \][/tex]
[tex]\[ T = 3 \text{ years} \][/tex]
However, the rate of interest [tex]\( R \)[/tex] is not provided. Without knowing the rate of interest (R), it is impossible to calculate the principal amount (P). Hence, the problem cannot be solved with the information given.
Therefore, the detailed solution is:
1. Identify the formula related to simple interest: [tex]\( A = P(1 + RT) \)[/tex].
2. Plug in the known values: [tex]\( A = 5525 \)[/tex], [tex]\( T = 3 \)[/tex].
3. Notice that [tex]\( R \)[/tex] (the rate of interest) is not provided.
4. Conclude that it is not possible to find [tex]\( P \)[/tex] without the value of [tex]\( R \)[/tex].
5. State that there is not enough information to solve for the principal amount [tex]\( P \)[/tex].
As a result, the final answer is that there is not enough information to solve for [tex]\( P \)[/tex] because the interest rate [tex]\( R \)[/tex] is missing.
