Let's solve the questions step by step.
### a. Calculation of Interest Earned
Markus has deposited [tex]$4,500 into his savings account, which pays an annual interest rate of 2% for 10 years. We will calculate the simple interest earned over this period using the formula:
\[ \text{Interest} = P \times R \times T \]
where:
- \( P \) is the principal amount (the deposit), which is $[/tex]4,500.
- [tex]\( R \)[/tex] is the annual interest rate, which is 2% or 0.02 in decimal form.
- [tex]\( T \)[/tex] is the time in years, which is 10 years.
Substitute the given values into the formula:
[tex]\[ \text{Interest} = 4500 \times 0.02 \times 10 \][/tex]
[tex]\[ \text{Interest} = 900 \][/tex]
So, the interest Markus will earn is [tex]$900.
### b. Calculation of Total Balance
To find the total balance in the account after 10 years, we need to add the initial savings, the deposit, and the interest earned together.
- Initial savings: $[/tex]3,000
- Deposit: [tex]$4,500
- Interest earned: $[/tex]900
Now, sum these amounts:
[tex]\[ \text{Total Balance} = \text{Initial Savings} + \text{Deposit} + \text{Interest Earned} \][/tex]
[tex]\[ \text{Total Balance} = 3000 + 4500 + 900 \][/tex]
[tex]\[ \text{Total Balance} = 8400 \][/tex]
So, the total balance in the account after 10 years is [tex]$8,400.
### Summary:
a. Markus will earn $[/tex]900 as interest over the 10-year period.
b. The total balance in the account after 10 years will be $8,400.
