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Benjamin invests
$400 in a savings account that earns
5% interest each year.
Which expression gives the balance in the account after 3 years?
Choose 1 answer:
(A)
400*0.05*0.05*0.05
(B)
400+(1+0.05)(1+0.05)(1+0.05)
(C)
400+0.05*0.05*0.05
(D)
400(1+0.05)(1+0.05)(1+0.05)

Benjamin invests $\$ 400$ in a savings account that earns $5 \%$ interest each year. $\newline$ Which expression gives the balance in the account after $3$ years? $\newline$ Choose $1$ answer: $\newline$ (A) $400 \cdot 0.05 \cdot 0.05 \cdot 0.05$ $\newline$ (B) $400+(1+0.05)(1+0.05)(1+0.05)$ $\newline$ (C) $400+0.05 \cdot 0.05 \cdot 0.05$ $\newline$ (D) $400(1+0.05)(1+0.05)(1+0.05)$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. Benjamin invests

\$ 400

in a savings account that earns

5 \%

interest each year.

\newline

Which expression gives the balance in the account after

3

years?

\newline

Choose

1

answer:

\newline

(A)

400 \cdot 0.05 \cdot 0.05 \cdot 0.05

\newline

(B)

400+(1+0.05)(1+0.05)(1+0.05)

\newline

(C)

400+0.05 \cdot 0.05 \cdot 0.05

\newline

(D)

400(1+0.05)(1+0.05)(1+0.05)

Identify Formula: Identify the formula for compound interest, which is $A = P(1 + r/n)^{(nt)}$ , 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. Since the problem does not specify the compounding frequency, we assume it is compounded once per year ( $n=1$ ). Therefore, the formula simplifies to $A = P(1 + r)^t$ .
Substitute Values: Substitute the given values into the simplified compound interest formula. Here, $P = \$400$ , $r = 5\%$ or $0.05$ as a decimal, and $t = 3$ years. So the expression becomes $A = 400(1 + 0.05)^3$ .
Check Answer Choices: Check the answer choices to see which one matches the expression $A = 400(1 + 0.05)^3$ . The correct choice is (D) $400(1+0.05)(1+0.05)(1+0.05)$ .

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