Questions: Calculate the amount of money you'll have at the end of the indicated time period, assuming that you earn simple interest. You deposit 3800 in an account with an annual interest of 4.6% for 5 years. The amount of money you'll have at the end of 5 years is . (Type an integer or a decimal.)

Calculate the amount of money you'll have at the end of the indicated time period, assuming that you earn simple interest. You deposit 3800 in an account with an annual interest of 4.6% for 5 years. The amount of money you'll have at the end of 5 years is . (Type an integer or a decimal.)
Transcript text: Calculate the amount of money you'll have at the end of the indicated time period, assuming that you earn simple interest. You deposit $\$ 3800$ in an account with an annual interest of $4.6 \%$ for 5 years. The amount of money you'll have at the end of 5 years is $\$$ $\square$ (Type an integer or a decimal.)
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Solution

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Solution Steps

Step 1: Identify the Parameters

The principal amount (P) is $3800, the annual interest rate (r) is 4.6%, and the time period (t) is 5 years.

Step 2: Apply the Simple Interest Formula

The formula to calculate the final amount using simple interest is: $$A = P(1 + rt)$$ where:

  • \(A\) is the final amount,
  • \(P\) is the principal amount (initial deposit),
  • \(r\) is the annual interest rate (expressed as a decimal),
  • \(t\) is the time in years.
Step 3: Substitute the Values into the Formula

Substituting the given values into the formula, we get: $$A = $3800(1 + 0.046 \times 5)$$

Step 4: Perform the Calculation

After performing the calculation, the final amount A is $4674.

Final Answer:

The final amount after 5 years, with an initial deposit of $3800 and an annual interest rate of 4.6%, is $4674.

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