Answer: $8802.82
Step-by-step explanation:
The formula to find the compound amount if the interest is compounded quarterly :-
[tex]A=P(1+\dfrac{r}{4})^{4t}[/tex], where P is the principal amount, r is the rate of interest( in decimal )and t is time (in years).
Given : P=$45,000 ; r= 6%=0.06 and t= 3 years
Then,
[tex]A=45000(1+\dfrac{0.06}{4})^{4\times3}\\\\\Rightarrow\ A=45000(1.015)^{12}\\\\\Rightarrow\ A=53802.8177158\approx\$53802.82[/tex]
Now, The compound interest is given by :-
[tex]I=A-P\\\\\Rightarrow\ I=53802.82-45000=\$8802.82[/tex]
Hence, the compound interest = $8802.82
