$($Complex annuity$)$ Upon graduating from college $35$ years$$ ago, Dr$.$ Nick Riviera was already thinking of retirement. Since then he has made deposits into his retirement fund on a weekly basis in the amount of $$$$20.$ Nick has just completed his final payment and is at last ready to retire. His retirement fund has earned $7\mathrm{.}4\%$ interest compounded weekly.

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

b$.$ In addition to all$$ this, $10$ years$$ ago, Nick received an inheritance check for $$$$20$ comma $000$ from his beloved uncle. He decided to deposit the entire amount into his retirement fund. What is his current balance in the$$ fund?

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Part $1$

a$.$ Since graduating from college $35$ years$$ ago, Dr$.$ Nick Riviera has made deposits into his retirement fund on a weekly basis in the amount of $$$$20.$ If his retirement fund has earned $7\mathrm{.}4\%$ interest compounded weekly$,$ how much has Nick accumulated in his retirement$$ account?