a $1,600 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?

Given is the Principal amount, P = 1600 dollars. Given the Annual interest is 7% i.e. r = 0.07 Given the Compounding period is semi-annually i.e. n = 2. Given is the Time of investment, t = 33 years. It says to find the Final Value of invested amount in the account after 33 years. We know the formula for Future Value of Money is given as follows :- [tex] Future \;\;Value = P*(1+\frac{r}{n})^{nt} \\\\
Future \;\;Value = 1600*(1+\frac{0.07}{2})^{(2*33)} \\\\
Future \;\;Value = 1600*(1+0.035)^{66} \\\\
Future \;\;Value = 1600*(1.035)^{66} \\\\
Future \;\;Value = 1600*(9.684185201) \\\\
Future \;\;Value = 15494.69632 \\\\
Future \;\;Value = 15,494.70 \;\;dollars [/tex]Hence, the final balance would be 15,494.70 dollars.