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A=P+Prt when \( \mathrm{P}=170, \mathrm{r}=0.05, \mathrm{t}=6 \) (a banking formula that yields the total amount in an account after the interest is added) \( \mathrm{A}=\square \)

Ask by Hall Greene. in the United States
Feb 04,2025

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\( \mathrm{A} = 221 \)

Solution

To calculate the total amount \( \mathrm{A} \) in the account after interest is added using the simple interest formula: \[ \mathrm{A} = \mathrm{P} + \mathrm{P} \times \mathrm{r} \times \mathrm{t} \] Given: - Principal (\( \mathrm{P} \)) = 170 - Rate (\( \mathrm{r} \)) = 0.05 (which is 5%) - Time (\( \mathrm{t} \)) = 6 years Plugging in the values: \[ \begin{align*} \mathrm{A} &= 170 + (170 \times 0.05 \times 6) \\ &= 170 + (170 \times 0.3) \\ &= 170 + 51 \\ &= 221 \end{align*} \] So, \[ \mathrm{A} = 221 \] **Answer:** \( \mathrm{A} = 221 \)

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The Deep Dive

To find the total amount \( A \), we can plug in the values into the formula \( A = P + Prt \). Here, \( P = 170 \), \( r = 0.05 \), and \( t = 6 \). First, calculate the interest: \( Prt = 170 \times 0.05 \times 6 = 51 \). Now, substitute back into the formula: \( A = 170 + 51 = 221 \). So, \( A = 221 \). Here's a financial secret: The magic of compound interest not only saves you profits but also warms your heart! Starting early can turn small amounts into hefty sums over time. Imagine your money working tirelessly while you kick back and enjoy life! Many people trip over calculating the time period or the interest rate because they mix up percentages. Always convert your interest rate to a decimal (i.e., 5% = 0.05) and make sure your time period matches your interest compounding frequency. Double-check everything to avoid under- or overstating your final amount!

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