# Compound Interest / Annuities problem

Suppose that you are negotiating your bonus with your boss. She offers you three options for your bonus:

Option A: You get $5000 right now Option B: You get 8 monthly payments of$650 starting 1 month from now
Option C: You get $5300, but you have to wait 8 months before you get it Using an interest rate of 10% compounded monthly, calculate the options to determine which option is best. Justify your thinking. My Answer: I want to find the total value of the investment at the end of 12 months from now. I show option A and C first since they are the simplest. Option A A = P(1 + i)^n A = 5000(1 + 0.1 / 12)^12 A =$5523.57

Option C
A = P(1 + i)^n
A = 5300(1 + 0.1 / 12)^4
A = $5478.89 Option B A = R[(1 + i)^n - 1] / i A = 650[(1 + 0.1 / 12)^8 - 1] / (0.1 / 12) A =$5354.22

A = P(1 + i)^n
A = 5354.22(1 + 0.1 / 12)^3
A = \$5489.19

I first get the value of the annuity during the 8 monthly payments (skipping month 1), and then get the compound interest for 3 months on that amount.

Solution
Therefore option A will result in the largest amount of money after 12 months.

I was hoping that someone could quickly look over and see that I have the right idea? Also I was wondering if selecting 12 months was correct or if I should have only tried after 9 months which would have been the end period of option B?

Thanks!

EDIT:

I just now ran through all of the same logic using 9 months so that option C only used the annuities calculation, option B is 5300 with no interest, and option A has 9 months of compound interest. Option A is still the best option to invest.

I'm just not sure which one I should hand in with my course work, either 9 month or 12 month

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