Final answer:
Using the compound interest formula A=P(1+(r/m))^(mt), the future value of a $12,000 investment at 2% interest compounded semiannually after 5 years is approximately $13,255.47.
Step-by-step explanation:
Calculating Compound Interest on Savings
To calculate the future value of an investment with compound interest, the given formula is used:
A = P(1 + (r/m))^(mt)
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
m is the number of times that interest is compounded per year.
t is the time the money is invested for in years.
For the given problem:
P = $12,000
r = 2% or 0.02
m = 2 (since the interest is compounded semiannually)
t = 5 years
Using the formula, we calculate the future value of the investment:
A = $12,000(1 + (0.02/2))^(2*5)
A = $12,000(1 + 0.01)^(10)
A = $12,000(1.01)^10
A = $12,000(1.104622125)
A = $13,255.47
This value is very close to the given option of $13,255, which suggests it is likely the correct amount assuming continuous compounding across full periods.