Question

Assuming no taxes is it better to take a 2,000,000 lump sum or 250,000 upfront and 200,000 for the next 10 years. Assume the prevailing intrust rate is .05 or 5%

Answer 1

No indication about the compounding frequency? Annual, quarterly, continuous?

Answer 2

Continuous

Answer 3

Are you still there?

Answer 4

Then we just have to calculate and compare. Your text might have a formula, but I'll just figure it out from scratch. The $2,000,000 lump sum generates the following amount:\[A_L(10)=2(10^6)e^{.5}\]The payment plan generates\[A_P(10)=(10^5)[2.5e^{.5} +2\sum_{k=0}^{9}2e^{.05k}]\]

Answer 5

Okay

Answer 6

As an intuitive guess, I'd say the lump sum will end up with more money, but you'll have to compute to be sure.

Answer 7

and how do I compute the second part...
i was planning on using PV=the definite integral f(t)e^(rt)dt

Answer 8

Actually, I have an extra factor of two in that formula; there should be one either before or after the summation, but not both.

Answer 9

My setup is based on being paid in $200,000 increments on the anniversary of the investment start date.

Answer 10

I understand I just dont know how to solve from there

Answer 11

It isn't hard, just a little tedious. Calculate e^(.05k) for k=1, 2, ...,9 and add them up. Multiply that by 200,000, add to the first term (the money from the first $250K) and compare it to the result of the first calculation (the one based on 2,000,000 for ten years).

Answer 12

Actually, you need to calculate for k=0, 1, 2, ..., 9