Question

PRESENT VALUE OF AN ANNUITY Find the present values of these annuities. First assume they are ordinary annuities, then assume they are annuities due

Compounding occurs once a year.

1. $400 per year for 10 years at 10%
2. $200 per year for 5 years at 5%
3. $400 per year for 5 years at 0%

Answer 1

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

1.Present value of annuity=$400[1-(1.1)^-10]/0.1

=$400*6.144567106

=$2457.83(Approx).

2.Present value of annuity=$200[1-(1.05)^-5]/0.05

=$200*4.329476671

=$865.90(Approx).

3.Present value of annuity=$400*5

=$2000

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

4..Present value of annuity=$2457.83*1.1

=$2703.61(Approx).

5.Present value of annuity=$865.90*1.05

=$909.19(Approx).

6.Present value of annuity=$400*5

=$2000