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

The total interest will Sergio earn on his investments at the end of 4 years 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 .

Principle = $4000

Rate = 3.2%

Time = 4 years

Put all the values in the formula

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

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

Simple interest = $ 512

Thus the simple interest for principle amount $4000 at the rate of interest 3.2% for 4 years is $512 .

Second part

Formula

`Amount = P(1 + (r)/(100))^(t)`

Amount = Principle + Interest

Where P is the principle , r is the rate of interest 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

r = 2.1%

t = 4 years

Put all the values in the formula

`Amount = 4000(1 + (2.1)/(100))^(4)`

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

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

`Amount = 4000* 1.08668`

Amount = $ 4346.72

Put in the formula

$4346.72 = $4000 + Interest

Interest = $4346.72 - $4000

Interest = $ 346.72

Thus the interest is for the principle amount $4,000 at the rate of interest 2.1% compounded annually for 4 year is $ 346.72 .

Third part

Formula

`Amount = P (1 + (r)/(400))^(4t)`

As given

$7,500 in a certificate of deposit earning 5% interest compounded quarterly for 4 years .

P = $7500

r = 5%

t = 4 years

Put all the values in the formula

`Amount = 7500(1 + (5)/(400))^(4* 4)`

`Amount = 7500(1 + (5)/(400))^(16)`

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

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

`Amount = 7500* 1.21989`

Amount = $ 9149.175

Put in the formula

$9149.175 = $7500 + Interest

Interest = $9149.175 - $7500

Interest = $ 1649.175

Thus the interest when principle amount $7500 at the rate of interest 5% compounded quarterly for 4 years is $ 1649.175 .

Thus

Total interest will Sergio earn = Simple interest + Compounded annually interest + Compounded quarterly interest

Put all the values in the above

Total interest will Sergio earn = $512 + $346.72 + $ 1649.175

= $ 2507.90 (Approx)

Therefore the total interest will Sergio earn on his investments at the end of 4 years is $2507.90 .

Option (d) is correct .

Answer 2

Well you need to use here the formula A = P(1 + r/n)nt
So
P = 4000 r = 2.1% = .021 n = 4 ... compounded quarterly, 4 times per year t = 4 ... number of years A = 4000(1 + .021/4)4(4) A = 4000(1.021)16 A = 4000(1.39447866269)
After doing the maths you need to subtract 4,000 and then you will find your answer. Hope this is useful