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:
- After 1 year: \( P + 80 = 1,080 \)
- 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.