Question

sergio has decided to diversify his investments in the following way:$4,000 in an account earning 3.2% simple interest$4,000 in a savings account earning 2.1% interest compounded annually$7,500 in a certificate of deposit earning 5% interest compounded quarterlyhow much total interest will sergio earn on his investments at the end of 4 years?

Answer 1

Answer: $1,208.28

Step-by-step explanation:

Formula we use here :-

Simple interest : $I=Prt$

Compound amount : $A=P(1+r)^t)$

Compound amount(Compounded quarterly):- $A=P(1+\dfrac{r}{4})^{4t})$

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 : $4000\times0.032\times4=\ 512$

2) $4,000 in a savings account earning 2.1% interest compounded annually

Compound Amount :- $A=4000(1+0.021)^4\approx\ 4346.73$

Compound interest : $A-P=\ 4346.73-\ 4000=\ 346.73$

3) $7,500 in a certificate of deposit earning 5% interest compounded quarterly

Compound Amount :- $A=4000(1+\dfrac{0.021}{4})^{4\times4}\approx\ 4349.56$

Compound interest : $A-P=\ 4349.56-\ 4000=\ 349.55$

Now, the total interest : $\ 512+\ 346.73+\ 349.55=\ 1208.28$

Hence, the total interest will sergio earn on his investments at the end of 4 years = $1,208.28

Answer 2

The formula for compound interest is : A = P(1+r/n)^nt

A = 4000 (1+0.021/4)^4x4

A = 4000 (1.021)^16

A = 5,577.91

Sergio's total interest would be : 5,577.91 - 4,000 = $ 1,577.91

hope this helps