Questions: Mariana has 50,000 in a savings account that earns 15% interest per year. The interest is not compounded. How much will she have in total in 5 years? Use the formula i = p r t, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Mariana has 50,000 in a savings account that earns 15% interest per year. The interest is not compounded. How much will she have in total in 5 years?

Use the formula i = p r t, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Transcript text: Mariana has $\$ 50,000$ in a savings account that earns $15 \%$ interest per year. The interest is not compounded. How much will she have in total in 5 years? Use the formula $i=p r t$, where $i$ is the interest earned, $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years.

Solution

Solution Steps

Step 1: Identify the given values

Principal $ p = 50,000 $
Interest rate $ r = 15\% = 0.15 $
Time $ t = 5 $ years

Step 2: Apply the simple interest formula

Use the formula $ i = p \cdot r \cdot t $ to calculate the interest earned over 5 years.

Step 3: Calculate the interest

Substitute the values into the formula: \[ i = 50,000 \cdot 0.15 \cdot 5 \] \[ i = 50,000 \cdot 0.75 \] \[ i = 37,500 \]

Step 4: Calculate the total amount

Add the interest earned to the principal: \[ \text{Total amount} = p + i \] \[ \text{Total amount} = 50,000 + 37,500 \] \[ \text{Total amount} = 87,500 \]

Final Answer

$\boxed{87,500}$

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