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 quarterly
How much total interest will Sergio earn on his investments at the end of 4 years?
a.
$1,240.82
b.
$2,123.90
c.
$2,497.17
d.
$2,507.90

Answer 1

A=4,000×(1+0.032×4)+4,000
×(1+0.021)^(4)+7,500×(1+0.05÷4)^(4×4)
=18,007.90

Interest earned
18007.90-15500==2,507.90

Answer 2

The total interest Sergio earns is $ 2507.90 .

Option (d) is correct .

Explanation:

First part

Formula

`Simple\ interest = (Principle* Rate* Time)/(100)`

As given

$4,000 in an account earning 3.2% simple interest for 4 years .

Put all the values in the formula

`Simple\ interest = (4000* 3.2* 4)/(100)`

`Simple\ interest = (51200)/(100)`

Simple interest = $512

Thus interest is $512 when invested $4000 in an account earning 3.2% for 4 years .

Second part

Formula

`Amount = P(1 + r)^(t)`

Amount = P + Interest

Where P is the principle , r is the rate of interest in the decimal form and t is the time in years .

As given

$4,000 in a savings account earning 2.1% interest compounded annually for 4 years .

P = $4000

2.1% is written in the decimal form

`= (2.1)/(100)`

= 0.021

r = 0.021

t = 4 year

Put all the values in the formula

`Amount = 4000(1 +0.021)^(4)`

`Amount = 4000(1.021)^(4)`

`Amount = 4000* 1.08668`

Amount = $4346.72

Thus

$4346.72 = $4000 + Interest

Interest = $4346.72 - $4000

Interest = $346.72

Thus interest is $346.72 when invested $4,000 in a savings account earning 2.1% for 4 years .

Third part

Formula

`Amount = P(1 +(r)/(4))^(4t)`

Amount = P + Interest

Where P is the principle , r is the rate of interest in the decimal form and t is the time in years .

As given

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

P = $7500

5% is written in the decimal form

`=(5)/(100)`

= 0.05

r = 0.05

t = 4 years

Put all the values in the formula

`Amount = 7500(1 +(0.05)/(4))^(4* 4)`

`Amount = 7500(1 +(0.05)/(4))^(16)`

`Amount = 7500(1 +0.0125)^(16)`

`Amount = 7500(1.0125)^(16)`

`Amount = 7500* 1.21989`

Amount = $9149.175

$9149.175 = $7500 + Interest

Interest = $9149.175 - $7500

Interest = $1649.175

Thus interest is $1649.175 when invested $7,500 in a certificate of deposit earning 5% for 4 years .

Thus

Total interest Sergio earns = Interest from simple interest + Interest from compounded annually + Interest from compounded quarterly .

Put all the value in the above

Total interest Sergio earns = $512 + $346.72 + $1649.175

= $ 2507.90 (Approx)

Therefore the total interest Sergio earns is $ 2507.90 .

Option (d) is correct .