Question

Find the present value of $600 due in the future under each of these conditions:

1. 12% nominal rate, semiannual compounding, discounted back 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.
   $   

2. 12% nominal rate, quarterly compounding, discounted back 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.
   $   

3. 12% nominal rate, monthly compounding, discounted back 1 year. Do not round intermediate calculations. Round your answer to the nearest cent.
   $   

Answer 1

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

600=P*(1+0.12/2)^(2*6)

P=600/(1+0.12/2)^(2*6)

=600*0.496969364

=$298.18(Approx)

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

600=P*(1+0.12/4)^(4*6)

P=600/(1+0.12/4)^(4*6)

=600*0.491933736

=$295.16(Approx)

c.We use the formula:  
A=P(1+r/12)^12n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

600=P*(1+0.12/12)^(12*1)

P=600/(1+0.12/12)^(12*1)

=600*0.887449225

=$532.47(Approx)