Use the compound interest formula to compute the total amount accumulated and the interest earned. $\$ 5000$ for $4$ years at $3.8 \%$ compounded monthly $\newline$ The total amount accumulated after $4$ years is $\$$ $\square$ $\newline$ (Round to the nearest cent as needed.) $\newline$ The amount of interest earned is $\$ \square$ . $\newline$ (Round to the nearest cent as needed.)

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Grade 8

Compound interest

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Q. Use the compound interest formula to compute the total amount accumulated and the interest earned.

\$ 5000

for

4

years at

3.8 \%

compounded monthly

\newline

The total amount accumulated after

4

years is

\$

\square

\newline

(Round to the nearest cent as needed.)

\newline

The amount of interest earned is

\$ \square

\newline

(Round to the nearest cent as needed.)

Question Prompt: Question_prompt: Calculate the total amount accumulated and the interest earned for $\$5000$ invested at $3.8\%$ compounded monthly for $4$ years.
Compound Interest Formula: Use the compound interest formula $A = P(1 + \frac{r}{n})^{nt}$ , where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.
Plug in Values: Plug in the values: $P = \$5000$ , $r = \frac{3.8}{100} = 0.038$ , $n = 12$ (since interest is compounded monthly), and $t = 4$ .
Calculate Amount Accumulated: Calculate the amount accumulated: $A = 5000(1 + 0.038/12)^{(12\times4)}$ .
Division Calculation: Do the division inside the parentheses: $0.038/12 = 0.0031667$ (rounded to $7$ decimal places).
Calculate Exponent: Calculate the exponent: $12 \times 4 = 48$ .
Substitute Values: Substitute the values into the formula: $A = 5000(1 + 0.0031667)^{48}$ .
Add Monthly Rate: Add $1$ to the monthly rate: $1 + 0.0031667 = 1.0031667$ .
Raise to Power: Raise to the $48^{\text{th}}$ power: $(1.0031667)^{48} \approx 1.160314$ (rounded to $6$ decimal places).
Multiply by Principal: Multiply by the principal: $A \approx 5000 \times 1.160314 \approx (\$)5801.57$ (rounded to the nearest cent).
Calculate Interest Earned: Subtract the principal from the total amount to find the interest earned: Interest = $A - P = \$5801.57 - \$5000 = \$801.57$ .