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Problem $5\mathrm{.}10($Present and Future Values for Different Interest Rates$)$

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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 $$400$ compounded for $10$ years at $4\%,$

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b$.$ An initial $$400$ compounded for $10$ years at $8\%.$

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c$.$ The present value of $$400$ due in $10$ years at $4\%.$

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d$.$ The present value of $$2,320$ 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?

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Assuming positive interest rates, the present value will increase as the interest rate increases.

Assuming positive interest rates, the present value will decrease as the interest rate increases.

Assuming positive interest rates, the present value will decrease as the interest rate decreases.

Assuming positive interest rates, the present value will not change as the interest rate increases.

Assuming positive interest rates, the present value will not change as the interest rate decreases.

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