Question

Find the present value of $75,000 that will be received in 5 years at the following discount rates:

(a) 3% annual compounding

(b) 6% semi-annual compounding

(c) 12% monthly compounding

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.

75000=P*(1.03)^5

P=75000/1.03^5

=$75000*0.862608784

=$64695.66(Approx).

b.

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

75000=P(1+0.06/2)^(2*5)

P=75000/(1+0.06/2)^(2*5)

=$75000*0.744093914

=$55807.04(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.

75000=P(1+0.12/12)^(12*5)

P=75000/(1+0.12/12)^(12*5)

=75000*0.550449615

which is equal to

=$41283.72(Approx).