Marlon has just won some money on a game show! He has the option to take a lump sum payment of $625,000 now or get paid an annuity of $4,500 per month for the next 15 years. Assuming the growth rate of the economy is 3.9% compounding annually over the next 15 years, which is the better deal for Marlon and by how much?

Question

anonymous · Answer

I think it's going to be the annuity but I've been having issues finding the Future Value of an Annuity

tkhunny · Answer

What's stopping you from calculating the Present Value of the Annuity Payments and simply comparing the Calculated PV with the $625,000?

anonymous · Answer

Do you know the future value of an annuity formula?

tkhunny · Answer

Why do you care about a Future Value?  $625,000 is NOW, not in the future.

i = 0.039 -- This is given in the problem statement.
j = i/12 = 0.00325 -- The 12 (monthly) is given in the problem statement.
v = 1/(1+j) -- Monthly Interest Discount Factor (or Inflation Factor)

PV of All Monthly Payments = $4500 + 4500v + 4500v^{2} + ... + 4500v^{180-1}$
$4,500 monthly is given in the problem statement.
180 months is given int eh problem statement as "15 years".

Add them all up!

PV of All Monthly Payments = $4500(1 + v + v^{2} + ... + v^{180-1})$

PV of All Monthly Payments = $4500\cdot \dfrac{1-v^{180}}{1-v}$

Can you see all that and can you then calculate the value?