Question

Cameron has decided to diversify his investments in the following way:
$3,000 in an account earning 2.7% simple interest
$5,000 in a savings account earning 1.8% interest compounded annually
$5,000 in a certificate of deposit earning 3.9% interest compounded quarterly
How much total interest will Cameron earn on his investments at the end of 3 years?
a.
$530.87
b.
$665.57
c.
$973.30
d.
$1,135.30

Answer 1

Answer: D

Step-by-step explanation:

Cameron has decided to diversify his investments in the following way:

$3,000 in an account earning 2.7% simple interest

$5,000 in a savings account earning 1.8% interest compounded annually

$5,000 in a certificate of deposit earning 3.9% interest compounded quarterly

How much total interest will Cameron earn on his investments at the end of 3 years?

a.

$530.87

b.

$665.57

c.

$973.30

d.

$1,135.30

Answer 2

Option (D) $1135.30, the total interest Cameron earn at the end of three years is the correct answer.

What is compound interest and simple interest?

Compound interest is calculated on the principle amount and the accumulated interest of previous periods. The principle amount keeps on varying during the entire borrowing period

Simple interest is calculated on the principle, or original amount of a loan. The principle amount is constant during entire period.

For the given situation,

1. $3,000 in an account earning 2.7% simple interest.

2. $5,000 in a savings account earning 1.8% interest compounded annually.

3. $5,000 in a certificate of deposit earning 3.9% interest compounded quarterly.

Let p be the principle

Let  r be the rate of interest

Let n be the number of years

Now consider the first investment,

$3,000 in an account earning 2.7% simple interest for three years

The formula for simple interest is

$S.I = pnr$

⇒ $S.I = (5000)(0.027)(3)$

⇒ $S.I= 243$

Now consider the second investment,

$5,000 in a savings account earning 1.8% interest compounded annually for three years.

Let A be the amount for the principle

Let n be number of times the amount is compounding

Let T be the time in years

The formula for compound interest,

$C.I=A-p$

$A=p(1+\frac{r}{n} )^{nT}$

⇒ $A=5000(1+\frac{0.018}{1} )^{3}$

⇒ $A=5000(1.018)^{3}$

⇒ $A=5274$

$C.I=A-P$

⇒ $C.I=5274-5000$

⇒ $C.I=274$

Now consider the third investment,

$5,000 in a certificate of deposit earning 3.9% interest compounded quarterly for three years

$A=p(1+\frac{r}{n} )^{nT}$

⇒ $A=5000(1+\frac{0.039}{4} )^{(4)(3)}$

⇒ $A=5000(1+0.00975)^{12}$

⇒ $A=5000(1.1234)$

⇒ $A=5617$

$C.I=A-P$

⇒ $C.I=5617-5000$

⇒ $C.I=617$

Thus Cameron's total interest on his investment,

⇒ $243+274+617$

⇒ $1134$

Hence we can conclude that option (D) $1135.30 is the correct answer.

Learn more about simple interest and compound interest here

https://brainly.com/question/13155407

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