Question

The first of ten semiannual payments of $2800 will be made 512512 years from today. What is the present value of this deferred annuity using a discount rate of 7.8% compounded semiannually? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

Firstly, we will calculate the EAR

EAR = ((1+(Nominal rate/Number of compounding periods)^ Number of compounding periods)  - 1

EAR= [(1+(7.8%/2)) ^2] - 1

EAR = 7.9521%

Now, we wil use a BA 2 plus calculator to find the PV of the semi annual payments 512512 years from today:

N: 10

I/Y: 7.9521%/ 2 = 3.976%

PMT: $2800

CMPT PV

THe PV we get 512512 years from now = 22,737.6093

PV Today = 22,737.6093/((1+7.9521%)^512512)

= 00.00