The problem asks us to find the future value of an annuity due. The payment is $900 per quarter, the interest rate is 9% compounded quarterly, and the term is 8.5 years.

1. Problem Description

The problem asks us to find the future value of an annuity due. The payment is $900 per quarter, the interest rate is 9% compounded quarterly, and the term is 8.5 years.

2. Solution Steps

First, we need to calculate the number of periods and the interest rate per period.

The number of years is $8.5$.

Since payments are made quarterly, the number of periods, $n$, is $8.5 \times 4 = 34$.

The annual interest rate is 9% or $0.09$.

Since interest is compounded quarterly, the interest rate per period, $i$, is $\frac{0.09}{4} = 0.0225$.

The future value of an annuity due formula is:

$FV = PMT \times \frac{(1+i)^n - 1}{i} \times (1+i)$

Where:

$FV$ = Future Value

$PMT$ = Payment per period = $900

$i$ = Interest rate per period = $0.0225

$n$ = Number of periods = $34

$FV = 900 \times \frac{(1+0.0225)^{34} - 1}{0.0225} \times (1+0.0225)$

$FV = 900 \times \frac{(1.0225)^{34} - 1}{0.0225} \times (1.0225)$

$FV = 900 \times \frac{2.155888 - 1}{0.0225} \times 1.0225$

$FV = 900 \times \frac{1.155888}{0.0225} \times 1.0225$

$FV = 900 \times 51.3728 \times 1.0225$

$FV = 900 \times 52.525952$

$FV = 47273.3568$

Rounding to the nearest cent, $FV = 47273.36$

3. Final Answer

$47273.36