Final answer:
Anjali's savings account with an initial investment of $8,455, a 7% interest rate compounded semi-annually, will grow to a balance of $15,235.26 after 8 years. The formula used for the calculation demonstrates the power of compound interest over time.
Step-by-step explanation:
Anjali wants to find the future value of her investment of $8,455 at a fixed annual interest rate of 7% compounded semi-annually over 8 years. The formula to calculate the future value of an investment compounded semi-annually is:
FV = P × (1 + r/n)nt
where:
- P = principal amount ($8,455)
- r = annual interest rate (7% or 0.07)
- n = number of times the interest is compounded per year (2 for semi-annual)
- t = number of years the money is invested (8 years)
By plugging in the values:
FV = $8,455 × (1 + 0.07/2)2×8
After calculating, the future value comes out to be:
FV = $8,455 × (1 + 0.035)16 = $8,455 × (1.035)16
The final balance Anjali will have in her savings account after 8 years will be:
FV = $8,455 × 1.802
FV = $15,235.26
This calculated final balance reflects the power of compound interest which effectively grows Anjali’s investment over the term of 8 years.