Answer:
To calculate how much Samantha will have in her bank account at the age of 57, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, Samantha's initial deposit is $2,000, the interest rate is 3% (or 0.03 in decimal form), she saves $800 per year, and the interest is compounded yearly.
First, let's calculate the total annual savings over two years:
Total savings = $800/year * 2 years = $1,600
Next, let's calculate the interest earned on the initial deposit and the total savings after two years:
Principal amount = $2,000
Interest rate = 3% = 0.03
Number of years = 2
A = (Principal amount + Total savings) * (1 + interest rate)^number of years
A = ($2,000 + $1,600) * (1 + 0.03)^2
Calculating this expression:
A = $3,600 * (1.03)^2
A = $3,600 * 1.0609
A ≈ $3,817.64
Therefore, Samantha will have approximately $3,817.64 in her bank account at the age of 57.