You own an ordinary annuity contract that will pay you $3,000 per year for 12 years.You need money to pay back a loan in 6 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 value of your 12-year annuity if paid in one lump sum five years from today?
A)$22,008
B)$18,000
C)$35,876
D)$38,880

Question

Quizplus · Accepted Answer

To find the lump sum value of the annuity, we need to calculate the Present Value (PV) of the annuity payments that will be received for the next 7 years (12 years - 5 years).

Using the formula for the Present Value of an Annuity:

PV = PMT x [(1 - (1 + r)^-n) / r]

Where: 
PMT = Payment per year = $3,000
r = interest rate per year = 8%
n = number of years = 7

PV = $3,000 x [(1 - (1 + 0.08)^-7) / 0.08] 
PV = $3,000 x [(1 - 0.5084) / 0.08] 
PV = $3,000 x [7.58] 
PV = $22,740

Therefore, the equivalent value of the 12-year annuity if paid in one lump sum five years from today is $22,740. Answer choice C is the closest to this value.

You Own an Ordinary Annuity Contract That Will Pay You