Question

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:
Choose 1 answer:
(Choice A)
\[400(1+0.05)(1+0.05)(1+0.05)\]
A
\[400(1+0.05)(1+0.05)(1+0.05)\]
(Choice B)
\[400+(1+0.05)(1+0.05)(1+0.05)\]
B
\[400+(1+0.05)(1+0.05)(1+0.05)\]
(Choice C)
\[400\cdot 0.05\cdot 0.05\cdot 0.05\]
C
\[400\cdot 0.05\cdot 0.05\cdot 0.05\]
(Choice D)
\[400+0.05\cdot 0.05\cdot 0.05\]
D
\[400+0.05\cdot 0.05\cdot 0.05\]

Answer 1

To find the balance in the account after 3 years with an initial investment of $400 at an interest rate of 5% per year, we can use the formula for compound interest.

The formula for the amount \( A \) accumulated after \( t \) years with an initial principal \( P \) and an interest rate \( r \) compounded annually is:

\[
A = P(1 + r)^t
\]

In this case, the variables are:
- \( P = 400 \)
- \( r = 0.05 \) (5%)
- \( t = 3 \)

Substituting these values into the formula, we get:

\[
A = 400(1 + 0.05)^3
\]

This can be simplified to:

\[
A = 400(1.05)(1.05)(1.05)
\]

Thus, the correct expression for the balance in the account after 3 years is:

**Choice A:**
\[400(1+0.05)(1+0.05)(1+0.05)\]