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Part $1$

$($Future value of an$$ annuity$)$Upon graduating from college $30$ years$$ ago, Dr$.$ Nick Riviera was already planning for his retirement. Since$$ then, he has made deposits into a retirement fund on a monthly basis in the amount of $$$$120.$ Nick has just completed his final payment and is at last ready to retire. His retirement fund has earned $12$ percent compounded monthly. 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$$ this, $10$ years ago Nick received an inheritance check for $$$$20,000$ from his beloved uncle. He decided to deposit the entire amount into his retirement fund. What is his current balance in the$$ fund?