Answer: $1,208.28
Step-by-step explanation:
Formula we use here :-
Simple interest : [tex]I=Prt[/tex]
Compound amount : [tex]A=P(1+r)^t)[/tex]
Compound amount(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 the time.
1) $4,000 in an account earning 3.2% simple interest
Simple interest : [tex]4000\times0.032\times4=\$512[/tex]
2) $4,000 in a savings account earning 2.1% interest compounded annually
Compound Amount :- [tex]A=4000(1+0.021)^4\approx\$4346.73[/tex]
Compound interest : [tex]A-P=\$4346.73-\$4000=\$346.73[/tex]
3) $7,500 in a certificate of deposit earning 5% interest compounded quarterly
Compound Amount :- [tex]A=4000(1+\dfrac{0.021}{4})^{4\times4}\approx\$4349.56[/tex]
Compound interest : [tex]A-P=\$4349.56-\$4000=\$349.55[/tex]
Now, the total interest : [tex]\$512+\$346.73+\$349.55=\$1208.28[/tex]
Hence, the total interest will sergio earn on his investments at the end of 4 years = $1,208.28
