Mathematics, 30.08.2019 00:40 kimho2324

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

Answers: 2

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Answers

Answer from: brebob3339

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

Option (d) is correct .

Step-by-step explanation:

First Part

Formula

$Simple\ interest = \frac{Principle\times Rate\times Time}{100}$

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

$Simple\ interest = \frac{4000\times 3.2\times 4}{100}$

$Simple\ interest = \frac{51200}{100}$

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

$Amount = P(1 + \frac{r}{100})^{t}$

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

$Amount = 4000(1 + \frac{2.1}{100})^{4}$

$Amount = 4000(1 +0.021)^{4}$

$Amount = 4000(1.021)^{4}$

$Amount = 4000\times 1.08668$

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

$Amount = P (1 + \frac{r}{400})^{4t}$

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

$Amount = 7500(1 + \frac{5}{400})^{4\times 4}$

$Amount = 7500(1 + \frac{5}{400})^{16}$

$Amount = 7500(1 +0.0125)^{16}$

$Amount = 7500(1.0125)^{16}$

$Amount = 7500\times 1.21989$

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 from: Quest

the perimeter is increased by a factor of 2

Answer from: Quest

step-by-step explanation:

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