I found this example problem in Eric V. Slud's "Actuarial Mathematics and Life-Table Statistics" book, but I'm having a hard time following it. I'm not sure if there's a typo, or if they just calculated the answer incorrectly, or what, but I'll share it with you here:

When I calculate the value in red, I get $52429.39 instead, which is a pretty noticeable difference.

Did they mean annuity due instead of immediate (a dot dot instead of just a)? I tried that, but I still get a different answer. Were they using a different interest rate? I don't understand.

**What's the correct answer here, and how do you get it?**
If this helps, I also get different answers for the following two calculations:

I don't understand how he's calculating the annuity value. It doesn't seem to follow from the formula.