Final answer:
To find out how much interest is earned on the account, one would calculate the future value of the initial deposit and the monthly deposits separately, and then subtract both the original contributions and the initial deposit from the total future value obtained.
Step-by-step explanation:
The student is asking how much interest would be earned by saving $2,000, plus an additional $100 each month for 10 years, with an annual interest rate of 2.5%. This is a compound interest problem, as the interest is likely to be compounded yearly, monthly, or daily depending on the account specifics. To solve this, we would use the formula for the future value of a series, which is often used in such savings calculations.
For simplicity, let's assume monthly compounding. The formula to calculate the future value of a series is:
FV = P * [(1 + r/n)^(nt) - 1] / (r/n)
Where:
FV is the future value of the investment,
P is the monthly payment,
r is the annual interest rate (in decimal),
n is the number of times the interest is compounded per year,
t is the time the money is invested for in years.
Calculating Total Accumulated Value
Given that P = $100, r = 0.025 (2.5%), n = 12 (monthly compounding), t = 10, and also considering the initial $2,000 deposit, the total amount would first be calculated using this formula and then the interest earned would be the total minus the initial deposit and the contributions ($100 * 12 months * 10 years).
Let's calculate:
Initial Investment Future Value (FV) = $2,000(1 + 0.025/12)^(12*10)
Monthly Deposits Future Value = $100 * [((1 + 0.025/12)^(12*10) - 1) / (0.025/12)]
Interest Earned
To find the interest earned, you subtract the total contributions and the initial $2,000 from the Future Value. Please note that depending on the specifics of the account, such as when interest is compounded, the actual figures might differ slightly when using a real calculator.