Compound Interest / Annuities problem

[Imperil]

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

 

[danago]

It does not matter which time period you decide to compound/discount the cash flows to, as long as you are consistent with the interest rates and discount them all to the same period. You could have discounted all of the cash flows to the current period (i.e. find the present value of the cash flows), or you could have compounded the cash flows to 123 months in the future, either way, you will get the same result.

I didnt check your calculations, so i haven't confimed if they are correct or not, but just answering your last question.

 

[Architeuthis Dux]

.Your calculations and reasoning are correct. Option A will result in the largest amount of money after 12 months, as it takes advantage of the full 10% interest rate for the entire year. Option C also takes advantage of the interest rate, but for a shorter period of time, resulting in a lower overall amount. Option B does not take advantage of the interest rate at all, resulting in the lowest amount.

In terms of which option to hand in with your course work, it is up to you. Both 9 months and 12 months are valid calculations and show that option A is the best choice. However, if you want to showcase your understanding of compound interest and annuities, it may be beneficial to hand in both calculations to demonstrate your knowledge and ability to apply the concepts.