Question

What is wrong with this question:
You borrow $15,000 at 6% for 5 years. what is the total cost of the loan. Use \(P_0(1+\frac{r}{n})^{nt}\)

Answer 1

How often is it compounded?

Answer 2

seen this not once, but 3 times just this afternoon!

Answer 3

it doesnt say if how its supposed to be compounded?

Answer 4

fine lets make it compounded monthly
that is how one usually pays a loan
still...

Answer 5

here was one example, i just answered two more

Answer 6

i am more and more convinced that \(75\%\) of high school math teachers do not belong anywhere near a classroom

Answer 7

any takers?

Answer 8

there are some well known assumptions when teaching financial algebra -
loan involves monthly payments called EMI's

Answer 9

you must clear the entire loan amount + accumulated interest in 5 years

Answer 10

right
simply put, this is the wrong @#$% formula!
if you invest \(\$15,000\) and \(6\%\) monthly then it will earn \[15,000(1+\frac{.06}{12})^{60}\] in 5 years ,but that has nothing to do with loan payments
the bank doesn't say "well we would have earned this much money, so you can pay is that"
it calculates loan payments which are entirely differnt!

Answer 11

what is weird is that this is a mistake i have seen people make, but not math teachers. and i saw this question, as i said, 3 times this evening
different question, identical dumb mistake

Answer 12

Exactly ! only the formula suggested to use is 100% misleading lol... otherwise question is okay

Answer 13

if i remember correctly the monthly payment would be something like
\[\frac{15,000\frac{.06}{12}}{1-(1+\frac{.06}{12})^{-60}}\]

Answer 14

yeah here it is

http://www.wolframalpha.com/input/?i=15000*%28+%280.06%2F12%281%2B0.06%2F12%29%5E%2812*5%29%29%2F%28+%281%2B0.06%2F12%29%5E%2812*5%29-1%29+%29

Answer 15

then you can calculate the total cost by multiplying by the number of payments i.e. 60

Answer 16

lol maybe the psychotic teacher wanted the student to derive the Monthly payment formula from the compound interest formula ?

Answer 17

total payments
http://www.wolframalpha.com/input/?i=60*15000*%28+%280.06%2F12%281%2B0.06%2F12%29^%2812*5%29%29%2F%28+%281%2B0.06%2F12%29^%2812*5%29-1%29+%29

Answer 18

amount you would have if you invested the money
http://www.wolframalpha.com/input/?i=15000%281%2B.06%2F12%29^60

Answer 19

Yeah i noticed the formula was wrong, i just assumed it was a simple question on not making monthly payments, just the value of the loan

Answer 20

yeah, but each question asked "how much would you pay over the course of the loan" except the one i attached, that asked "when will the loan be $1000?" or something like that
very weird
i will stop ranting now

Answer 21

\(0 = \left(\left(P(1+\dfrac{r}{12}) - M\right)(1+\dfrac{r}{12})-M\right)(1+\dfrac{r}{12})-M ...... 60 ~times\)

Eventhough its a simple geometric series, derivation is not trivial for a highschool student. Its just the carelessness from the teacher side...