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a$.$ You plan to make five deposits of $$1,000$ each, one every $6$ months, with the first payment being made in $6$ months. You will then make no more deposits. If the bank pays $10\%$ nominal interest, compounded semiannually, how much will be in your account after $3$ years? Do not round intermediate calculations. Round your answer to the nearest cent.

b$.$ One year from today you must make a payment of $$5,000.$ To prepare for this payment, you plan to make two equal quarterly deposits $($at the end of Quarters $1$ and $2)$ in a bank that pays $10\%$ nominal interest compounded quarterly. How large must each of the two payments be$?$ Do not round intermediate calculations. Round your answer to the nearest cent.

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