Sure! Let's solve this step by step:
1. Understanding the Problem:
- Mr. Smith deposited an amount (principal) of [tex]$5,200.00 in a bank.
- The time period for which the money is deposited is 3 years.
- The annual interest rate is 8%.
2. Identifying the Formula:
- The formula to calculate simple interest is:
\[
\text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\]
where:
- Principal (P) is the initial amount of money deposited, which is $[/tex]5,200.00.
- Rate (R) is the annual interest rate, which should be expressed as a decimal. An 8% rate is equivalent to 0.08.
- Time (T) is the duration for which the money is deposited, which is 3 years.
3. Substitute the Values into the Formula:
- Principal (P) = [tex]$5,200.00
- Rate (R) = 8% per annum = 0.08
- Time (T) = 3 years
\[
\text{Simple Interest} = 5200.00 \times 0.08 \times 3
\]
4. Perform the Calculation:
- Multiply principal by the rate:
\[
5200.00 \times 0.08 = 416.00
\]
- Then multiply the result by the time (years):
\[
416.00 \times 3 = 1248.00
\]
5. Conclusion:
- The simple interest earned by Mr. Smith at the end of 3 years is $[/tex]1,248.00.
So, the simple interest Mr. Smith would earn on his deposit of [tex]$5,200.00 at a rate of 8% per annum over 3 years would be $[/tex]1,248.00.
