Answer:
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
[tex]Simple\ interest = \frac{Principle\times Rate\times Time}{100}[/tex]
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
[tex]Simple\ interest = \frac{4000\times 3.2\times 4}{100}[/tex]
[tex]Simple\ interest = \frac{51200}{100}[/tex]
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
[tex]Amount = P(1 + \frac{r}{100})^{t}[/tex]
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
[tex]Amount = 4000(1 + \frac{2.1}{100})^{4}[/tex]
[tex]Amount = 4000(1 +0.021)^{4}[/tex]
[tex]Amount = 4000(1.021)^{4}[/tex]
[tex]Amount = 4000\times 1.08668[/tex]
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
[tex]Amount = P (1 + \frac{r}{400})^{4t}[/tex]
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
[tex]Amount = 7500(1 + \frac{5}{400})^{4\times 4}[/tex]
[tex]Amount = 7500(1 + \frac{5}{400})^{16}[/tex]
[tex]Amount = 7500(1 +0.0125)^{16}[/tex]
[tex]Amount = 7500(1.0125)^{16}[/tex]
[tex]Amount = 7500\times 1.21989[/tex]
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 .
