Question

Calculate the present value of $6,000 received five years from today if your investments pay (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

	Present Value a. 7 percent compounded annually b. 9 percent compounded annually c. 11 percent compounded annually d. 11 percent compounded semiannually e. 11 percent compounded quarterly

Answer 1

a.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

6000=P*(1.07)^5

P=6000/1.07^5

=6000*0.712986179

=$4277.92(Approx).

b.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

6000=P*(1.09)^5

P=6000/1.09^5

=$6000*0.649931386

=$3899.59(Approx).

c.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

6000=P*(1.11)^5

P=6000/1.11^5

=$6000*0.593451328

=$3560.71(Approx).

d.We use the formula:
A=P(1+r/200)^2n
where
A=future value
P=present value
r=rate of interest
n=time period.

6000=P*(1+0.11/2)^(2*5)

P=6000/(1+0.11/2)^(2*5)

=$6000*0.585430579

=$3512.58(Approx).

e.We use the formula:
A=P(1+r/400)^4n
where
A=future value
P=present value
r=rate of interest
n=time period.

6000=P*(1+0.11/4)^(4*5)

P=6000/(1+0.11/4)^(4*5)

=$6000*0.581250566

which is equal to =$3487.50(Approx).