Solution:
The formula for compound interest, including principal sum, is:
[tex]A = p(1 + \frac{r}{n})^{nt}[/tex]
Where,
A = the future value of the investment
P = the principal investment amount\
r = the annual interest rate in decimal
n = the number of times that interest is compounded per unit t
t = the time the money is invested
From given,
p = 4000
t = 5
[tex]r = 11 \% = \frac{11}{100} = 0.11[/tex]
n = 4 ( compounded quarterly )
Substituting the values in formula,
[tex]A = 4000(1 + \frac{0.11}{4})^{4 \times 5}\\\\ A = 4000( 1.0275)^{20}\\\\A = 4000 \times 1.720428\\\\A = 6881.7137 \approx 6881.71[/tex]
Thus the final amount is $ 6881.71
