Given in the question:
a.) Joe planned to invest $3,500.
b.) The account will earn an annual interest rate of 9.8% years at the end of 20 years.
c.) It is compounded quarterly.
To be able to determine how much profit will he make, we will be using the formula for Compounded Interest.
[tex]\text{ Compound Interest = }P(1\text{ + }\frac{\frac{r}{100}}{n})^{nt}\text{ - P}[/tex]
Where,
P = Principal Amount = $3,500
r = Interest Rate = 9.8%
n = Number of times interest is compounded = Quarterly = 4
t = Time = 20 years
Let's now plug in the values,
[tex]\text{ Compound Interest = }P(1\text{ + }\frac{\frac{r}{100}}{n})^{nt}\text{ - P}[/tex][tex]\text{= }(3,500)(1\text{ + }\frac{\frac{9.8}{100}}{4})^{(4)(20)}\text{ - 3,500}[/tex][tex]\text{ = }(3,500)(1+0.0245)^{80}\text{ - 3,500}[/tex][tex]\text{ = }(3,500)(1.0245)^{80}\text{ - 3,500}[/tex][tex]\text{ = }(3,500)(6.9335718282)\text{ - 3,500}[/tex][tex]\text{ = 24,267.5013987 - 3,500}[/tex][tex]\text{Compound Interest = 20,767.50139884 }\approx\text{ \$20,767.50}[/tex]
Therefore, Joe will make a profit of $20,767.50
