I'm not quite sure which formula to use when answering this word problem. Is the question asking me to find the future value of a dollar or the future value of an annuity?
Any help would be greatly appreciated!


Word Problem:
The Treasurer of a major corporation has invested some of the company's excess cash in a real estate fund that buys office buildings and rents the space. The find is planning to sell some the buildings and has given the Treasurer an option of a lump sum payout or payments over 26 years as the buildings are sold. The lump sum payout would be $6,256,450 or the payments would be received annually to total $15 million at the end of 26 years. The treasurer needs to let the fund know what option is best for the corporation.


Question: There should be calculations for the cash option earning a return of 8%, 10%, and 12%. Use the same returns for the payments and calculate the difference between the two choices. Ignore taxes.






I used this formula to calculate the future value of a dollar: FV = PV(1+i)^n to calculate the amount the particular percent would accumulate to over 26 years.

8% for 26 years
FV = PV(1+i)^n
FV = 6,256,450(1+.08)26
FV = 6,256,450(7.4)
FV = $46,274,914.05

However, if it's about an annuity, I'd have to use this formula:
FV = PV[(1+i)^n - 1/ I ]

I'm supposed to have a factor somewhere in there, but I can probably figure that out once I know if it's an annuity or not.

Am I on the right track?

Is the question asking me to find the future value of a dollar or the future value of an annuity?

Both.


The lump sum payout would be $6,256,450 or the payments would be received annually to total $15 million at the end of 26 years.

I'm assuming they're meaning 26 equal payments that add up to $15 million. Meaning you need to figure out what a payment for one year is going to be. You have two options and you're ignoring the payment option.


8% for 26 years
FV = PV(1+i)^n
FV = 6,256,450(1+.08)26
FV = 6,256,450(7.4)
FV = $46,274,914.05

That's correct. But it only accounts for the lump sum payment. You also have to figure out the future value of the series of payments over 26 years. Then you are going to compare the future values of these two options to see which has a higher future value.


I'm supposed to have a factor somewhere in there, but I can probably figure that out once I know if it's an annuity or not.

The "factor" is the (1+i)^n and the (1-(1+i)^-n)/i. When the term "factor" is used, it's generally referring to a number off a set of charts. Those factors are just this part of your equation, already done for an amount of $1, and thrown together into a big chart. Then people can just look them up and multiply and not mess with all this algebra. But since you're doing algebra, you're not going to be looking up any factors.


Am I on the right track?

Yes, you just missed a few of those big nails.