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

a$.$ An initial $$300$ compounded for $10$ years at $4\%.$

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b$.$ An initial $$300$ compounded for $10$ years at $8\%.$

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c$.$ The present value of $$300$ due in $10$ years at $4\%.$

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d$.$ The present value of $$1,620$ due in $10$ years at $8\%$ and $4\%.$

Present value at $8\%$:$

Present value at $4\%$:$

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?