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