Pregunta
Alark inverts \( \$ 1,000 \) at \( 6 \% \) simple interest for 5 yean How much is in the account at the end of the 5 yeans pertod? Answen \( \$ \square \)
Ask by Cross Willis. in the United States
Feb 03,2025
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After 5 years, the account will have \$1,300.
Solución
To calculate the amount in the account after 5 years with simple interest, you can use the simple interest formula:
\[
\text{A} = \text{P} \times (1 + \text{r} \times \text{t})
\]
Where:
- \(\text{A}\) = the amount of money accumulated after \( t \) years, including interest.
- \(\text{P}\) = principal amount (\$1,000)
- \(\text{r}\) = annual interest rate (6% or 0.06)
- \(\text{t}\) = time the money is invested for (5 years)
Plugging in the values:
\[
\text{A} = 1000 \times (1 + 0.06 \times 5) = 1000 \times (1 + 0.30) = 1000 \times 1.30 = \$1,300
\]
**Answer:** \$1,300
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The Deep Dive
To calculate the total amount in the account at the end of 5 years, we can use the formula for simple interest: \[ \text{Total Amount} = \text{Principal} + \text{Interest} \] \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] For Alark's investment, the interest earned would be: \[ \text{Interest} = 1000 \times 0.06 \times 5 = 300 \] Now, add the interest to the principal: \[ \text{Total Amount} = 1000 + 300 = 1300 \] So, at the end of the 5 years, the total amount in the account is \( \$1,300 \).
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