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Find the following values. Compounding$/$discounting occurs annually. Do not round intermediate calculations. Round your answers to the nearest cent.

a$.$ An initial $$600$ compounded for $10$ years at $10\%.$

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b$.$ An initial $$600$ compounded for $10$ years at $20\%,$

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c$.$ The present value of $$600$ due in $10$ years at $10\%.$

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d$.$ The present value of $$2,830$ due in $10$ years at $20\%$ and $10\%.$

Present value at $20\%$:$

Present value at $10\%$:$

e$.$ Define present value.

I. The present value is the value today of a sum of money to be received in the future and in general is less than the future value.

II$.$ The present value is the value today of a sum of money to be received in the future and in general is greater than the future value.

III. The present value is the value today of a sum of money to be received in the future and in general is equal to the future value.

IV$.$ The present value is the value in the future of a sum of money to be received today and in general is less than the future value.

$v.$ The present value is the value in the future of a sum of money to be received today and in general is greater than the future value.

How are present values affected by interest rates?