$($Future value of an annuity$)$ Upon graduating from college $35$ years ago, Dr$.$ Nick Riviera was already planning for his

retirement. Since then, he has made deposits into a retirement fund on a semiannually basis in the amount of $$900.$

Nick has just completed his final payment and is at last ready to retire. His retirement fund has earned $7$ percent

compounded semiannually. Use five decimal places for the periodic interest rate in your calculations.

a$.$ How much has Nick accumulated in his retirement account?

b$.$ In addition to this, $20$ years ago Nick received an inheritance check for $$20,000$ from his beloved uncle. He decided

to deposit the entire amount into his retirement fund. What is his current balance in the fund?