Final answer:
The future value of a $10,000 investment at 3% annual interest compounded over 5 years is approximately $11,592.74.
Step-by-step explanation:
The student has asked about the future value of a savings account with an interest rate. This question involves understanding compound interest which is a financial concept in mathematics used to calculate the future value of an investment based on the principal and the compounded rate of interest over time.
To find the future value of an initial $10,000 deposit in a savings account at a 3% annual interest rate after 5 years, we can use the compound interest formula:
FV = P(1 + r)^n
Where FV is the future value, P is the principal amount ($10,000), r is the annual interest rate (3% or 0.03), and n is the number of times the interest is compounded per year (once, for annual compounding).
Sampling this into the formula, we get:
FV = 10,000(1 + 0.03)^5
Calculating this gives us:
FV = 10,000(1.159274)^5
Thus, FV = $11,592.74
After 5 years, the future value of the investment would be approximately $11,592.74.