Question

You own an 5 year, 5 1/2% simple interest bearing note with a face value (principal) of $15,000. Three months before the due date of the note you need some money due to an unexpected emergency and decide to sell the note to a friend. If your friend wants to earn 8% simple interest on their investment, how much should your friend agree to pay you for the note? Round your answer off to the nearest whole dollar.

Answer 1

holy crap thats a long problem

Answer 2

Haha, yes I know...

Answer 3

@mayankdevnani a little help plz

Answer 4

I know that
S = ?
P = $15,000
R = 0.055
T = 5 years

S = P + PRT
So, S = 15,000 + (15,000)(0.055)(5) = 19125

Answer 5

If FV is the final value of your interest bearing note after 3 months, then your friend wants to buy it at a price FP (friend price) such that \[FV = 1.08(FP)\]Solve for FP:\[FP = \frac{FV}{1.08}\]You are already given everything you need to caculate FV:\[FV=P(1+rt) = (15000)(1+(0.055)(5)) = 19125\]So \[FP = \frac{19125}{1.08} = 17708.33\]

Answer 6

Shouldn't the 3 months figure into the calculation above?

Answer 7

I don't see how it would. It would only affect your own profit/loss, not your friend's.

Answer 8

Thats what I was confused about because in a previous example she gave us the time that "friend 2" had the one was factored into the equation..

Answer 9

The friend should buy it at such a price that in 3 months they would cash it for $19,125 yielding them an effective interest of 8%.

Answer 10

x + x * 1/4 * .08 = 19,125 (3 months is 1/4th of a year).
solve for x

Answer 11

Friend's Principal = x
simple interest = 8% = 0.08
time invested = 3 months = 1/4 year
Final Amount = $19,125

Solve for x using the simple interest formula.

Answer 12

So, would it be $18,750?

Answer 13

I think so.

Answer 14

That would evaluate to x=18750. But if the friend spends 18750, then an 8% profit would bring it to 18750*1.08=20250, which is greater than the final value.

Answer 15

No, but the friend will be cashing it in 3 months. What you calculated is after one year.

Answer 16

The interest is 8% per annum. So you get the 8% only if you wait for 1 year.

Answer 17

I guess it depends on if the 8% is supposed to be total profit or an annual rate. I interpreted it as a total profit, so 8% gained in just 3 months.

Answer 18

8% simple interest implies 8% per year.

Answer 19

Thank you both for your help, I will let you know if I got it right :)