Question

Your best friend who owns an annuity that promises to pay $1,000 at the end of each year, for 20 years, comes to you and offers to sell you all of the payments to be received after the 10th year for a price of $7,000. With an APR of 2.3% compounded quarterly, should you pay the $7,000 today to receive payment numbers 11 and onwards? Additionally, is he/she a good friend? Justify your answer (Note: If you buy the annuity, you will receive 10 payments of $1,000)

Answer 1

We need to find the PV of the $1000 annuity
receivable from year 11 to 20.
Let us find the PV of the Annuity on the 10 th year
Formula for present value of an anuuity = PV= A [ {(1+k)n-1}/k(1+k)n]
PV = Present value of Annuity
A = periodical Yearly payment =$1000
k=interest rate=2.32% per year
n=periods=10years
EAR =2.3% compounded Qtrly =(1+2.3%/4)^4-1=	2.320%	pa
PV =1000*[(1.0232^10-1)/(2.32%*1.0232^10)
PV =$8,834.03
So PV of Annuity at Year 10 =$8834.03
We need to discount it @2.32% for 10 years
to get the PV today.
PV of Annuity today =8834.03/1.0232^10=	$        7,023.50
The friend is offering $7,000 for the Annuity
So $7,000 is a fir price for the Annuity and it can be accepted.
We can say that the friend is a good and relaible friend.