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

Explanation:

Formula we use here :-

Simple interest :
`I=Prt`

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

Compound amount(Compounded quarterly):-
`A=P(1+(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*0.032*4=\$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+(0.021)/(4))^(4*4)\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