Question

You own an annuity due contract that will pay you $3,000 per year for 12 years. You need money to pay back a loan in 5 years, and you are afraid if you get the annuity payments annually you will spend the money and not be able to pay back your loan. You decide to sell your annuity for a lump sum of cash to be paid to you five years from today. If the interest rate is  8%, what is the equivalent your 12 year annuity if paid in one lump sum five years from today?

•  $35,876

•  $22,008

•  $38,880

•  $18,000

Answer 1

Equivalent value of 12 year annuity if paid in one lump sum five years from today=3000/8%*(1-1/1.08^12)*1.08*1.08^5
=35876.426102

Answer 2

SOLUTION :

Discount rate = 8% = 0.08

=> 1 + r = 1.08

PV of annuity due ($3000 per year for 12 years at discount rate 0f 8%) :

= 3000(1.08)(1.08^12 - 1)/(0.08*1.08^12)

= 24416.893 ($)

FV in 5 years = 24416.893*1,08^5 = 35876.43 ($)  = 35876 ($) approx.

So, equivalent of annuity due is the lump sum paid 5years from today 

= $35,876 = Option A (ANSWER)