Question

Which of these can be represented by the expression
?

A.
the balance of a savings account after t years if the initial balance is $500 and it is invested at a 3.5% annual interest rate compounded annually

B.
the balance of a savings account after t years if the initial balance is $500 and it is invested at a 0.875% annual interest rate compounded annually

C.
the balance of a savings account after t years if the initial balance is $500 and it is invested at a 0.875% annual interest rate compounded quarterly

D.
the balance of a savings account after t years if the initial balance is $500 and it is invested at a 3.5% annual interest rate compounded quarterly

Answer 1

choose one answer

Answer 2

To determine which options can be represented by the expression \( A = P(1 + r/n)^{nt} \), where:

- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial balance).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.

Let's analyze each option:

**A.** The balance of a savings account after \( t \) years if the initial balance is $500 and it is invested at a 3.5% annual interest rate compounded annually.

- Here, \( P = 500 \), \( r = 0.035 \), \( n = 1 \) (compounded once a year).
- This can be represented as:
\[
A = 500(1 + 0.035/1)^{1 \cdot t}
\]

**B.** The balance of a savings account after \( t \) years if the initial balance is $500 and it is invested at a 0.875% annual interest rate compounded annually.

- Here, \( P = 500 \), \( r = 0.00875 \), \( n = 1 \).
- This can be represented as:
\[
A = 500(1 + 0.00875/1)^{1 \cdot t}
\]

**C.** The balance of a savings account after \( t \) years if the initial balance is $500 and it is invested at a 0.875% annual interest rate compounded quarterly.

- Here, \( P = 500 \), \( r = 0.00875 \), \( n = 4 \) (because it is compounded quarterly).
- This can be represented as:
\[
A = 500(1 + 0.00875/4)^{4t}
\]

**D.** The balance of a savings account after \( t \) years if the initial balance is $500 and it is invested at a 3.5% annual interest rate compounded quarterly.

- Here, \( P = 500 \), \( r = 0.035 \), \( n = 4 \).
- This can be represented as:
\[
A = 500(1 + 0.035/4)^{4t}
\]

Based on the analysis:

- Option A can be represented by the formula.
- Option B can be represented by the formula.
- Option C can be represented by the formula.
- Option D can be represented by the formula.

Thus, all four options (A, B, C, and D) can be represented by the expression given.

Answer 3

Given the requirement to choose just one answer based on the provided expression \( A = P(1 + r/n)^{nt} \) for different scenarios, the most straightforward representation is:

**A.** the balance of a savings account after \( t \) years if the initial balance is $500 and it is invested at a 3.5% annual interest rate compounded annually.

This option represents the simplest case where interest is compounded annually (\( n = 1 \)), making it the clearest fit for the expression.