Find the present values of these ordinary annuities. discounting occurs once a year.

a. $600 per year for 12 years at 8%

The formula for future annuity is given by:

FV=P[ (1+r) ^n-1]/r

where:

FV-future value

P=principle

r=rate

n=time

thus given that:

p=$600, n=12 years, r=8%

The future value annuity of this amount will be:

FV=600[ (1+0.08) ^12-1]/0.08

simplifying the above we get:

FV=$11,386.28

Thus the present value of this amount will be calculated using compounding formula:

A=P (1+r) ^n

the terms are defined as above

thus plugging our values and solving for P we get

11386.28=P (1+0.08) ^12

simplifying this we get:

P=$4521.65

Hence the present value of this annuity is $4521.65