Question

A) end of 20 year compound quarterly'sB) how much profit did Joe make in this investment

Answer 1

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.

`\text{ Compound Interest = }P(1\text{ + }((r)/(100))/(n))^(nt)\text{ - P}`

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,

`\text{ Compound Interest = }P(1\text{ + }((r)/(100))/(n))^(nt)\text{ - P}`
`\text{= }(3,500)(1\text{ + }((9.8)/(100))/(4))^((4)(20))\text{ - 3,500}`
`\text{ = }(3,500)(1+0.0245)^(80)\text{ - 3,500}`
`\text{ = }(3,500)(1.0245)^(80)\text{ - 3,500}`
`\text{ = }(3,500)(6.9335718282)\text{ - 3,500}`
`\text{ = 24,267.5013987 - 3,500}`
`\text{Compound Interest = 20,767.50139884 }\approx\text{ \$20,767.50}`

Therefore, Joe will make a profit of $20,767.50