Questions: A retiree invests 3,000 in a savings plan that pays 4% per year. What will the account balance be at the end of the first year?

Solution Steps

To solve this problem, we need to calculate the account balance at the end of the first year using the simple interest formula. The formula for simple interest is:

\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

where:

• Principal is the initial amount of money invested ($3,000 in this case).
• Rate is the annual interest rate (4% or 0.04 as a decimal).
• Time is the time period in years (1 year in this case).

The account balance at the end of the year will be the sum of the principal and the interest earned.

Using the simple interest formula:

\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

we substitute the values:

\[ \text{Interest} = 3000 \times 0.04 \times 1 = 120.0 \]

The account balance at the end of the year is given by:

\[ \text{Account Balance} = \text{Principal} + \text{Interest} \]

Substituting the values we have:

\[ \text{Account Balance} = 3000 + 120.0 = 3120.0 \]

Final Answer