Just won a lottery jackpot of $11,000,000. You will be paid in 26 equal annual installments beginning immediately. If you had the money now, you could invest it in an account with a quoted annual interest rate of 9% with monthly compounding interest. What is the present value of the payments you will receive?

Question

Wheeler

Mathematics

28 April, 07:50

Just won a lottery jackpot of $11,000,000. You will be paid in 26 equal annual installments beginning immediately. If you had the money now, you could invest it in an account with a quoted annual interest rate of 9% with monthly compounding interest. What is the present value of the payments you will receive?

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Juliana Owens · Answer 1

The formula for the present value of an anuallity is:

PV = A * [ 1 - (1 + r) ^ (-n) ] / r

Here:

A = 11000000 / 26 = 423076.92

r is the effective rate of 9% monthly compounded

r = (1 + 0.09/12) ^ (12) - 1 = 1.0938 - 1 = 0.0938

n = 26

Then, PV = 423,076.92 * [1 - (1+0.0938) ^ (-26) ] / (0.0938)

PV = 4,072,055.25