Question

Present value of a annuity. Find the present values of these ordinary annuities. Discounting occurs once a year.

$400 per year for 10 years at 10%.

$200 per year for 5 years at 5%.

$400 per year for 5 years at 0%.

REWORK PARTS A,B,C assuming they are annuities due.

Answer 1

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

a.Present value=400/1.1+400/1.1^2+........+400/1.1^10

=400[1/1.1+1/1.1^2+..........+1/1.1^10]

=400*6.144567106

=$2457.83(Approx)

2.Present value=200/1.05+200/1.05^2+...........+200/1.05^5

=$200[1/1.05+1/1.05^2+..........+1/1.05^5]

=$200*4.329476671

=$865.90

3.Present value=400*5

=$2000

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

4.Present value=2457.83*1.1

=$2703.61

5.Present value=865.9*1.05

=$909.19

6.Present value=$400*5

=$2000