Given:
Principal amount = $2000
Rate of interest = 3.5% compounded quarterly.
Time = 6 years
To find:
The amount after 6 years.
Solution:
The formula for amount after compound interest is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is principal, r is rate of interest in decimal, n is the number of time interest compounded in an year and t is the number of years.
The interest is compounded quarterly, so [tex]n=4[/tex].
Substituting [tex]P=2000,r=0.035,n=4,t=6[/tex], we get
[tex]A=2000\left(1+\dfrac{0.035}{4}\right)^{4(6)}[/tex]
[tex]A=2000\left(1+0.00875\right)^{24}[/tex]
[tex]A=2000\left(1.00875\right)^{24}[/tex]
[tex]A=2465.10340[/tex]
Approximate the value to the nearest hundredth.
[tex]A\approx 2465.10[/tex]
The amount after 6 years us $2465.10. Therefore, the correct option is A.
