Final answer:
After 25 years, an initial deposit of $9,500 with a 3.4% interest rate compounded semi-annually will grow to approximately $26,024.90 using compound interest.
Step-by-step explanation:
To calculate the future value of an account with an initial deposit that earns a fixed interest rate compounded at regular intervals, we use the formula for compound interest:
FV = P (1 + r/n)^(nt)
Where FV is the future value, P is the principal amount (initial deposit), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years the money is invested.
For the given scenario:
- P = $9,500 (initial deposit)
- r = 3.4% or 0.034 (annual interest rate in decimal)
- n = 2 (compounded semi-annually)
- t = 25 years
Plugging these values into the compound interest formula:
FV = 9500 (1 + 0.034/2)^(2*25)
FV = 9500 (1 + 0.017)^(50)
FV = 9500 (1.017)^50
FV = 9500 * (2.73946323)
FV = $26,024.90
So, after 25 years, the account with an initial deposit of $9,500 that earns 3.4% interest compounded semi-annually will be worth approximately $26,024.90.