Question

2. (Annuity present value) Calculate the present value of an annuity of $6,500 per year. Assume the discount rate is 7%.
(a) In case of the first cash flow received today and the last one received 3 years from today? (b) In case of the first cash flow received a year from today and the last one received 4 years from today? (c) In case of the first cash flow received two years from today and the last one received 4 years from today?

Answer 1

The present value of an annuity of $6,500, for three different cases is calculated as follows.

Case-A: The generalized expression for calculating the present value of annuity

FV FV FV PV FV+71+*1+r)2 (1r) FV (1r)

Where, PV=present value, FV=Future value, r=discount rate, n=number of years

using above formula for case-A

FV FV FV PV FV+1+r) (1 r) (1)3 2

6500 6500 6500 PV 65007(1+0.07) (1+0.07)2 (1+0.07)3

PV=$23558.24

Case-B:

FV FV FV FV PV =1 (1+r) (1+3 (1+r)4 2

6500 6500 6500 6500 PV (1+0.07 + (10.07)2 (10.07) (10.07)4

PV=$22020.07

Case-C:

FV FV FV PV = 1+ r )2 (1+r)3 (1+r)|

6500 6500 6500 PV + (10.07)3 (10.07)4 (10.07)2

PV=$15945.3