Answer: $59313.58
Step-by-step explanation:
We know that formula we use to find the accumulated amount of the annuity ( ordinary annuity interest is compounded ) is given by :-
[tex]FV=A(\frac{(1+\frac{r}{m})^{mt})-1}{\frac{r}{m}})[/tex], where A is the annuity payment deposit, r is annual interest rate , t is time in years and n is number of periods.
Given : Annuity payment deposit :A= $4500
rate of interest :r= 6%=0.06
No. of periods : m= 1 [∵ its annual]
Time : t= 10 years
Now we get,
[tex]FV=(4500)(\frac{(1+\frac{0.06}{1})^{1\times10})-1}{\frac{0.06}{1}})\\\\\Rightarrow\ FV=(4500)(\frac{(1.06)^{10})-1}{0.06})\\\\\Rightarrow\ FV=(4500)(\frac{0.79084769654}{0.06})\\\\\Rightarrow\ FV=(4500)(13.1807949423)\\\\\Rightarrow\ FV=59313.5772407\approx59313.58 \ \[/tex]
∴ the accumulated amount of the annuity= $59313.58
