Question

Calculate the present value of the following annuity streams:

a. $4,000 received each year for 5 years on the last day of each year if your investments pay 8 percent compounded annually.
b. $4,000 received each quarter for 5 years on the last day of each quarter if your investments pay 8 percent compounded quarterly.
c. $4,000 received each year for 5 years on the first day of each year if your investments pay 8 percent compounded annually.
d. $4,000 received each quarter for 5 years on the first day of each quarter if your investments pay 8 percent compounded quarterly.

Answer 1

Present value of Annuity ordinary annuity=Annuity payment*((1-(1/(1+r)^n))/r)

where

r-intrest rate per period

n-number of periods

Present value of Annuity due=Annuity payment*((1-(1/(1+r)^n))/r)*(1+r)

r-intrest rate per period

n-number of periods

a. This is ordinary annuity

r-8%

n-5

Annuity payment=4000

Present value of Annuity ordinary annuity=4000*((1-(1/(1+.08)^5))/.08)

=$15970.84

b  This is ordinary annuity

r-8/4=2% Per quarter

n-5*4=20

Annuity payment=4000

Present value of Annuity ordinary annuity=4000*((1-(1/(1+.02)^20))/.02)

=$65405.73

c

This is annuity due

r-8%

n-5

Annuity payment=4000

Present value of Annuity due=4000*((1-(1/(1+.08)^5))/.08)*(1+.08)

=$17248.51

d.

This is annuity due

r-8/4=2% Per quarter

n-5*4=20

Annuity payment=4000

Present value of Annuity due=4000*((1-(1/(1+.02)^20))/.02)*(1+.02)

=$66713.85

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