Question

Find the present value of $725 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

15% nominal rate, semiannual compounding, discounted back 5 years. $

15% nominal rate, quarterly compounding, discounted back 5 years. $

15% nominal rate, monthly compounding, discounted back 1 year.

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

725=P*(1+0.15/2)^(2*5)

P=725/(1+0.15/2)^(2*5)

=725*0.485193928

=$351.77(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.

725=P*(1+0.15/4)^(4*5)

P=725/(1+0.15/4)^(4*5)

=725*0.478892342

=$347.2(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.

725=P*(1+0.15/12)^(12*1)

P=725/(1+0.15/12)^(12*1)

=725*0.8615086

=$624.59(Approx).