Question

Find the present value of $200 due in the future under each of these conditions:

16% nominal rate, semiannual compounding, discounted back 5 years. Round your answer to the nearest cent.

$

16% nominal rate, quarterly compounding, discounted back 5 years. Round your answer to the nearest cent.

$

16% nominal rate, monthly compounding, discounted back 1 year. Round your answer to the nearest cent.

$

Answer 1

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

200=P(1+16/200)^(2*5)

P=$200/(1+16/200)^(2*5)

=92.64(Approx)

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

200=P(1+16/400)^(4*5)

P=$200/(1+16/400)^(4*5)

=$91.28(Approx)

3.

We use the formula:
A=P(1+r/1200)^12n
where
A=future value
P=present value
r=rate of interest
n=time period.

200=P(1+16/1200)^(12*1)

P=$200/(1+16/1200)^(12*1)

=$170.61(Approx).