Question

Suppose you are going to receive $12,000 per year for five years. The appropriate interest rate is 9 percent. a-1. What is the present value of the payments if they are in the form of an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a-2. What is the present value of the payments if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b-1. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b-2. What is the future value if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c-1. Which has the higher present value, the ordinary annuity or annuity due? c-2. Which has the higher future value?

Answer 1

What is the present value of the payments if they are in the form of an ordinary annuity?

Discount all cash flows

12,000/1.09=11,009

12,000/1.09^2=10,100

12,000/1.09^3=9,266

12,000/1.09^4=8,501

12,000/1.09^5=7,799

Add all these discounted cash flows= $46,675 is the present value of ordinary annuity

a-2. What is the present value of the payments if the payments are an annuity due?

In an annuity due payment is made at the beginning of the year so we subtract one from each compounding period so,

12,000/1.09^0=12,000

12,000/1.09=11,009

12,000/1.09^2=10,100

12,000/1.09^3=9,266

12,000/1.09^4=8,501

add all these discounted cash flows = $50,876= PV of annuity due

FV of ordinary annuity

PV= 0

PMT=12,000

I= 9

N= 5

FV=? Put these in financial calculator= $71,816

Fv of annuity due=

12,000+

PV=0

PMT=12,000

I=9

N=4

FV=?=66,877

Pv of annuity due is higher and FV or ordinary annuity is higher.

Step-by-step explanation: