Question

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 8%.

$  

b. An initial $400 compounded for 10 years at 16%.

$  

c. The present value of $400 due in 10 years at 8%.

$  

d. The present value of $1,265 due in 10 years at 16% and 8%.

Present value at 16%: $  

Present value at 8%: $  

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?

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

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

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

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

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

Answer 1

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

$  

Solution:

Future Value = Initial amount x (1+Rate)^Years

Future Value = 400 x (1+8%)^10

Future Value = $863.57

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b. An initial $400 compounded for 10 years at 16%.

$  

Solution:

Future Value = Initial amount x (1+Rate)^Years

Future Value = 400 x (1+16%)^10

Future Value = $ 1764.57

--------------------------

c. The present value of $400 due in 10 years at 8%.

$  

Solution:

Present Value = Future Value / (1+Rate)^Years

Present Value = 400 / (1+8%)^10

Present Value = $185.28

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d. The present value of $1,265 due in 10 years at 16% and 8%.

Present value at 16%: $

Solution:

Present Value = Future Value / (1+Rate)^Years

Present Value = 1265 / (1+16%)^10

Present Value = $286.75

AND ------------

Present value at 8%: $  

Solution:

Present Value = Future Value / (1+Rate)^Years

Present Value = 1265 / (1+8%)^10

Present Value = $ 585.94

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e. Define present value.

Correct option is > 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.

--------------------------------

How are present values affected by interest rates?

Note: There is some issue because I read two options correct and they are same.

Correct option is > b. or c.

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

Or

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