There are a couple of ways of approaching this problem:
1) Because the payments are made every 2nd year, will assume that they are deposited at the END of the year, it is always easiest to make the interest rate MATCH the deposits. Since the interest rate is 8% compounded annually, will simply compound it for two years. So, we have: 1.08^2 =1.1664 -1 x 100 =16.64%. Now, will use the common formula for FV of $1 per period, or:
FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD.
FV =5,000 x [1 + 0.1664]^20 - 1 / 0.1664
FV =5,000 x 124.5464
FV =$622,732.02 - which is what he would expect to have in his retirement account.
2) The 2nd approach is find the equivalent ANNUAL payments, using the exact same formula above and solve for payments as follows:
5,000 = P x 1.08^2 - 1 / 0.08
5,000 =P x 0.1664 / 0.08
5,000 =P x 2.08
P =2,403.85 equivalent annual payments. Then, we use the above formula for 40 years.
FV =2,403.85 x [1.08]^40 - 1 /0.08
FV =$622,733.02, which is the same as above. $1's difference is due to rounding off the annual payments.