Stephen invests $2,000 in a savings account paying 6% annual interest. Find the balance after 5 years if the interest is compounded quarterly.

The balance of Stephen's savings account after 5 years is US$ 2,693.71

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Investment = US$ 2,000

Annual interest rate = 6% compounded quarterly = 1.5% per quarter

Duration of the investment = 5 years = 20 quarters

2. Let's find the future value of this investment after 5 years or 20 quarters, using the following formula:

FV = PV * (1 + r) ⁿ

PV = Investment = US$ 2,000

rate (r) = 1.5% = 0.015

number of periods (n) = 20

Replacing with the real values, we have:

FV = 2,000 * (1 + 0.015) ²⁰

FV = 2,000 * 1.015 ²⁰

FV = 2,000 * 1.34685501

FV = US$ 2,693.71