Question

Find the following values. Compounding/discounting occurs annually. Round your answers to the nearest cent.

a. An initial $600 compounded for 10 years at 3%.$  

b. An initial $600 compounded for 10 years at 6%.$  

c. The present value of $600 due in 10 year at 3%.$  

d. The present value of $2,655 due in 10 years at 6%.$  

e. The present value of $2,655 due in 10 years at 3%.$  

Define present value.

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.

-Select one

How are present values affected by interest rates?

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 rates increases.

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

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.

Answer 1

Future Value = Present Value*((1+r)^t)

where r is the interest rate and t is the time period in years.

a)

Present value

600

r

0.03

t

10

Future value

600*((1.03)^10)

Future value

806.35

b)

Present value

600

r

0.06

t

10

Future value

600*((1.06)^10)

Future value

1074.51

Present Value = Future value/ ((1+r)^t)

where r is the interest rate and t is the time period in years.

c)

Future value

600

r

0.03

t

10

Present value

600/((1.03)^10)

Present value

446.46

d)

Future value

2655

r

0.06

t

10

Present value

2655/((1.06)^10)

Present value

1482.54

e)

Future value

2655

r

0.03

t

10

Present value

2655/((1.03)^10)

Present value

1975.57

(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?

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

The bond prices are the sum of the present values of future cash flows.

When interest rates rise bond prices fall because the present value of future cash flows

will decrease as the interest rates increase.