Question

5.15

Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

1. $300 per year for 16 years at 8%.

   $  

2. $150 per year for 8 years at 4%.

   $  

3. $900 per year for 8 years at 0%.

   $  

4. Rework previous parts assuming they are annuities due.

   Present value of $300 per year for 16 years at 8%: $  

   Present value of $150 per year for 8 years at 4%: $  

   Present value of $900 per year for 8 years at 0%: $  

Answer 1

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

1.Present value=300[(1.08)^16-1]/0.08

=300*30.324283

=$9097.28(Approx).

2.Present value=150[(1.04)^8-1]/0.04

=150*9.21422626

=$1382.13(Approx).

3.Present value=900*8

=$7200

Present value of annuity due=Present value of annuity*(1+rate)

1.Present value=9097.28*1.08

=$9825.07(Approx).

2.Present value=1382.13*1.04

=$1437.42(Approx).

3.Present value=900*8

=$7200