Question

You plan to put $10,000 into your retirement account at the start. Write an equation to represent the total amount of money that is in your account after t years
A=_____ x______
$10,000
(1 + 5.75/1) ^ t
(1 + 0.0575/1) ^ t
(1 + 5.75t)
(1 + 0.0575t)

Answer 1

To represent the total amount of money \( A \) in your retirement account after \( t \) years with an initial investment of $10,000 and an annual interest rate of 5.75%, you would use the formula for compound interest.

The general formula for compound interest is:

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

where:
- \( A \) is the total amount of money after \( t \) years,
- \( P \) is the principal amount (the initial investment),
- \( r \) is the annual interest rate (as a decimal), and
- \( t \) is the number of years the money is invested or borrowed.

In your case:
- \( P = 10,000 \)
- \( r = 5.75\% = 0.0575 \)

Using these values, the equation can be written as:

\[
A = 10,000(1 + 0.0575)^t
\]

So, filling in the blanks provided, the equation will be:

\[
A = 10,000 \times (1 + 0.0575)^t
\]

This is the correct representation of the total amount of money in your account after \( t \) years.