Which of the following statements are correct concerning the present value of $1.00 five years from today discounted at 5%? I. The present value is equal to $1.00 divided by 1.05 to the 5th power. II. If the discount rate were less than 5%, the present value would be smaller. III. If the discount rate were more than 5%, the present value would be smaller. IV. If the $1.00 were to be received 6 years from today, the present value would be larger.

1 and 3 option

Explanation:

Which of the following statements are correct concerning the present value of $1.00 five years from today discounted at 5%?  The present value is equal to $1.00 divided by 1.05 to the 5th power and If the discount rate were more than 5%, the present value would be smaller.

To calculate present value:The present value is equal to $1.00 divided by 1.05 to the 5th power, Therefore

Present value= the future value/(1+r)n    where n=5, r= 0.005 or 0.006

which will be 1/(1+0.05)5

                           =0.78

Note:The present value interest factor for a single sum is always equal to or less than 1 and the further in time, the smaller the present value interest factor

Statements I and III

Explanation:

I)

Using the formula

Present value= Future value/(1+r)^n

where:

future value= $1

r is the interest rate,

n is the investment time period

Present value= 1/(1+5%)^5 (raise to the 5th power)

=$0.78

Note that ideally the value of a dollar should be less in the future using the time call value of money factor. Thus this statement is correct.

III)

If the discount rate is less than 5% to achieve a future value of $1.00 at the end of 5 years, the present value should be bigger.

Assume the discount rate is 4.9%

Present value=

1/(1+4.9%)^5 (raise to the 5th power)

=1/(1+0.045)^5

=1/1.049^5

=$1.27 (Correct since the present value is bigger)

c is the correct answer.