Mathematics: 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

Step-by-step explanation:I believe it is b...

Sergio has decided to diversify his investments

Ответ:

mazolethrin9632

14.01.2022

Mathematics

The total interest Sergio earns 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 .

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 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

$= \frac{2.1}{100}$

= 0.021

r = 0.021

t = 4 year

Put all the values in the formula

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

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

$Amount = 4000\times 1.08668$

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

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

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

$=\frac{5}{100}$

= 0.05

r = 0.05

t = 4 years

Put all the values in the formula

$Amount = 7500(1 +\frac{0.05}{4})^{4\times 4}$

$Amount = 7500(1 +\frac{0.05}{4})^{16}$

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

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

$Amount = 7500\times 1.21989$

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 .

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