Question

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 4%.

$  

b. An initial $600 compounded for 10 years at 8%.

$  

c. The present value of $600 due in 10 years at 4%.

$  

d. The present value of $2,655 due in 10 years at 8% and 4%.

Present value at 8%: $  

Present value at 4%: $  

e. 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?

Answer 1

a)
FV = PV * (1+r)^n
= $600 * (1 + 4%)^10
= $888.15

Future value = $888.15

b)
FV = PV * (1+r)^n
= $600 * (1 + 8%)^10
= $1,295.35

Future value = $1,295.35

c)
PV = FV / (1+r)^n
= $600/ (1+4%)^10
= $405.34

Present value - $405.34

d)
Present value at 8%:

PV = FV / (1+r)^n
= $2,655 / (1+8%)^10
= $1,229.78

Present value = $1,229.78

Present value at 4%:

PV = FV / (1+r)^n
= $2,655 / (1+4%)^10
= $1,793.62

Present value = $1,793.62

e)
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.

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