Suppose that $2000 is invested at a rate of 2.6%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 9 years.

The total amount after 9 years of US$ 2,000 invested at a rate of 2.6% compounded quarterly is US$ 5,038.89

Step-by-step explanation:

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

Investment amount = US$ 2,000

Duration of the investment = 9 years = 36 quarters

Annual interest rate = 2.6% compounded quarterly

2. Let's find the future value of this investment after 9 years or 36 quarters, using the following formula:

FV = PV * (1 + r) ⁿ

PV = Investment = US$ 2,000

number of periods (n) = 36 (number of quarters in 9 years)

rate (r) = 3% = 0.026

Replacing with the real values, we have:

FV = 2,000 * (1 + 0.026) ³⁶

FV = 2,000 * (1.026) ³⁶

FV = 2,000 * 2.51944561

FV = 5,038.89 (Rounding to two decimal places)