Answer: To find the value of the annuity for the indicated monthly deposit amount, number of deposits, and interest rate, we can use the following formula:
```A = PMT * ((1 + r/n)^(nt) - 1) / (r/n)```
Where:
- A is the value of the annuity
- PMT is the monthly deposit amount
- r is the interest rate
- n is the number of compounding periods per year
- t is the total number of years
In this case, the values are:
- PMT = $150 (monthly deposit amount)
- r = 0.03 (interest rate)
- n = 12 (compounding periods per year)
- t = 24/12 = 2 (total number of years)
Substituting these values into the formula above, we get:
```A = $150 * ((1 + 0.03/12)^(12*2) - 1) / (0.03/12)```
Simplifying this expression gives us:
```A = $150 * (1.0275^24 - 1) / 0.0025```
Evaluating this gives us:
```A = $3,789.09```
Therefore, the value of the annuity is $3,789.09.
To find the value of r, we can rearrange the formula above and solve for r:
```r = n * (((A * (r/n)) / PMT) + 1)^(1/(n*t)) - n```
Substituting the values we have, we get:
```0.03 = 12 * (((3789.09 * (0.03/12)) / 150) + 1)^(1/(12*2)) - 12```
Solving this equation gives us:
```r = 0.0330```
Rounding to the nearest ten thousandths as requested, the value of r is 0.0330.