Final answer:
After 8 years of investing $3,500 with a 16% nominal annual interest rate compounded semi-annually, you will have $13,416.52.
Step-by-step explanation:
When you invest money with compound interest, the amount of money you have after a certain period depends on the initial principal, the interest rate, and the frequency of compounding. In this case, you've invested $3,500 at a 16% nominal annual rate, compounded semi-annually. To calculate the future value of this investment after 8 years, we will use the compound interest formula: FV = P × (1 + r/n)nt
Where:
FV is the future value of the investment,
P is the principal amount ($3,500),
r is the annual interest rate (0.16),
n is the number of times interest is compounded per year (2),
t is the number of years the money is invested (8).
Plugging in the numbers, we calculate the future value:
FV = $3,500 × (1 + 0.16/2)(2×8)
FV = $3,500 × (1 + 0.08)16
FV = $3,500 × (1.08)16
FV = $3,500 × 3.83329 (rounded to five decimal places)
FV = $13,416.515
Therefore, after 8 years, you will have $13,416.52 in the account.