Question

se the table to answer the question.

Determining the initial deposit prior to annual increments.
Years Amount
1 $1,080
2 $1,160
3 $1,240
The table shows the amount of money in a bank account after a certain number of years. What is the initial value?

Answer 1

To determine the initial deposit prior to annual increments, we can analyze the amounts given for each year.

From the table, we can see the following:

- After 1 year, the amount is $1,080.
- After 2 years, the amount is $1,160.
- After 3 years, the amount is $1,240.

The increments from one year to the next can be calculated:

- From year 1 to year 2: $1,160 - $1,080 = $80
- From year 2 to year 3: $1,240 - $1,160 = $80

This shows that the amount grows by $80 each year.

Now, if we work backwards to find the initial deposit (let's call it \( P \)), we can set up the following equations based on the amounts for each year:

1. After 1 year: \( P + 80 = 1,080 \)
2. After 2 years: \( P + 80 + 80 = 1,160 \)

From the first equation:

\[
P + 80 = 1,080
\]
\[
P = 1,080 - 80
\]
\[
P = 1,000
\]

So, the initial deposit prior to annual increments is **$1,000**.

We can verify this with the second year calculation:

Starting amount (initial deposit) = $1,000
After 1 year: $1,000 + $80 = $1,080 (matches the table)
After 2 years: $1,080 + $80 = $1,160 (matches the table)
After 3 years: $1,160 + $80 = $1,240 (matches the table)

Thus, the initial deposit is confirmed to be **$1,000**.