Determining the initial deposit prior to annual increments.

Question

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 amount prior to the annual increments of the bank account, we can analyze the amounts given in the table.

The amounts after each year are:

• Year 1: $1,080
• Year 2: $1,160
• Year 3: $1,240

From the table, we can see that the account increases by $80 each year. Thus, we can denote the initial deposit as \( P \) and the annual increment as \( D = 80 \).

The amounts for each year can be represented as follows:

1. After Year 1: \[ P + (1 \times D) = P + 80 = 1080 \]

2. After Year 2: \[ P + (2 \times D) = P + 160 = 1160 \]

3. After Year 3: \[ P + (3 \times D) = P + 240 = 1240 \]

Let's solve for \( P \) using the first equation: \[ P + 80 = 1080 \] Subtracting 80 from both sides: \[ P = 1080 - 80 = 1000 \]

Now we can verify using the second and third equations:

For Year 2: \[ 1000 + 160 = 1160 \] This is correct.

For Year 3: \[ 1000 + 240 = 1240 \] This is also correct.

Thus, the initial deposit amount is: \[ \boxed{1000} \]