To determine the balance after 1 year in a savings account with an initial investment of [tex]$1,550 and a 4.2% simple interest rate, we need to calculate the interest earned and then add that to the initial investment.
First, let's understand what simple interest is. Simple interest is calculated with the formula:
\[ \text{Interest} = P \times r \times t \]
where:
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time the money is invested for (in years).
Given:
- \( P = 1,550 \) dollars,
- \( r = 4.2\% = 0.042 \),
- \( t = 1 \) year.
We already have the interest calculated as $[/tex]65.10. Now, to find the balance after 1 year, we need to add this interest to the initial investment:
[tex]\[ \text{Balance} = \text{Initial Investment} + \text{Interest} \][/tex]
So,
[tex]\[ \text{Balance} = 1,550 + 65.10 \][/tex]
Adding these values:
[tex]\[ \text{Balance} = 1,615.10 \][/tex]
Therefore, the balance after 1 year in the savings account is $1,615.10.
