Well, Jim must be pretty lucky to afford to deposit $2,000 every 2nd year into his pension fund! Now, let's crunch some numbers and see what we get.
First, let's break down the problem. Jim has 20 years to accumulate money in his private pension fund, and it offers a 5% interest rate compounded annually. He can deposit $2,000 at the end of every 2nd year. We want to find out how much he can accumulate in this period.
To solve this problem, we can use the future value of an ordinary annuity formula:
FV = P * [(1 + r)^N - 1] / r,
where FV is the future value, P is the payment amount, r is the interest rate, and N is the number of periods.
Now, let's plug in the values into the formula:
P = $2,000,
r = 5% (0.05),
N = 20 / 2 = 10 (since Jim deposits every 2nd year).
FV = $2,000 * [(1 + 0.05)^10 - 1] / 0.05.
Calculating this expression, we get:
FV = $2,000 * [1.62889462677744] / 0.05
= $3,257.79.
Well, it seems like my calculations might match your textbook, but not exactly your given answer of $32,259. That's quite a difference!
To be honest, either your textbook made a mistake, or Jim has some secret pension fund that I'm not aware of. Perhaps he invested in a "Magical Unicorn Pension Plan" with increasing interest rates and rainbows as returns. In that case, $32,259 might just be possible!
On a serious note, it's always a good idea to double-check the calculations, and if you're still not getting the correct answer, it might be worth consulting with your teacher or instructor for further clarification.