Let's solve the problem step by step.
We have the following information:
- Principal amount (P): $3611
- Annual interest rate (R): 5.34% or 0.0534 (in decimal form)
- Time period (T): 2 months, which we need to express in years. Since there are 12 months in a year, 2 months is \(\frac{2}{12}\) or \(\frac{1}{6}\) years.
First, we calculate the amount of simple interest earned using the formula for simple interest:
[tex]\[ \text{Simple Interest} = P \times R \times T \][/tex]
Plugging in the values:
[tex]\[ \text{Simple Interest} = 3611 \times 0.0534 \times \frac{1}{6} \][/tex]
The interest earned comes out to $32.14 when rounded to the nearest cent.
Next, we find the maturity value, which is the sum of the principal amount and the interest earned. The formula for maturity value (A) is:
[tex]\[ A = P + \text{Simple Interest} \][/tex]
So,
[tex]\[ A = 3611 + 32.14 \][/tex]
Therefore, the maturity value is $3643.14 when rounded to the nearest cent.
To summarize:
- The amount of simple interest earned is $32.14.
- The maturity value is $3643.14.
