SOLUTION: A friend of your sells his car to a college student and take a personal note for 1200$ with no interest, payable at 100$ per month for 12 months. Your Friend immediately approaches

Question 1190991: A friend of your sells his car to a college student and take a personal note for 1200$ with no interest, payable at 100$ per month for 12 months. Your Friend immediately approaches you and offers to sell you this note. how much should you pay for the note if you want an annual yield of 12% on your investment.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if you buy the note, you will receive 100 dollars a month for 12 months.
at the end of the 12 months, you want to have earned 12% on your investment.

assuming you do nothing with the money except collect it, then at the end of the 12 month period you will have 1200 dollars.
take that 1200 and divide it by 1.12 and you get 1200/1.12 = 1071.428571.
that's how much you should offer to pay for the note.

there are multiple things you can do with the money once you receive it, but those considerations should not impact what you are willing to pay for the loan.
you could save it in an interest bearing account, you could spend it on different things, you could just put it in a drawer and wait until it accumulate to its full value.
at 0% interest on the loan, the full value will be 1200 at the end of the loan period.
that's what you will have if you do nothing with the money but hold on to it.

if you pay 1071.428571 for the note, then at the end of 12 months you will have 1200 and your return on your investment will be 1200 / 1071.428571 = 12%.

no additional consideration is given as to what you will do with the money after you receive it.

one additional consideration might be:
assume you can invest the payments at 6% per year compounded monthly.
the future value of that investment would be equal to 1233.556237.
divide that by 1.12 to get a present value of 1101.389498.
you could offer 1101.389498 for the note, assuming that you will invest the proceeds at 6% per year compounded monthly.
your return on y9ur investment will be 1233.556237 / 1101.389498 = 1.12.

bottom line:

if you do re-invest the money after you receive it and you with to earn 12% per year on your investment, then offer 1071.1071.428571 for the note.

if you assume you will be investing the money at 6% per year compounded monthly, and you wish to earn 12% per year on your investment, then offer 1101.389498.
your friend will be happier and you will still be able to earn 12% per year on your investment.

what you do with the money after you receive it can have a very large impact on what you're willing to offer.
your most conservative offer assumes you will not invest the money after you receive it.
in fact, unless he's a very good friend, that's the offer you should make.
there really should be no consideration of what you do with the money after you receive it.

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