Question

Please help & show ALL steps! Will give a medal and fan for best answer!

Your uncle loaned you some money and did not charge interest. The amount you owe him at the end of each of the first 5 months is $937.50, $875.00, $812.50, $750.00, and $687.50. If the pattern continues, how much will you still owe him at the end of one year?

Answer 1

@Hollywood_Undead, my notifications say that you replied to this but I can't see any comments!

Answer 2

i replied??

Answer 3

That's what my thing says lol.

Answer 4

@whpalmer4

Answer 5

how weird xD haha idk i dont think i did

Answer 6

Lol it is weird! I thought my computer was messing up or something haha.

Answer 7

i mean it kinda called me out like i was supposed to do this question xD

Answer 8

since there is no interest ... the amount this person pays to his uncle for a month is a constant...

by taking the difference of values of 2 months , u can find that amount....

can u find it ?

Answer 9

Compare the terms in the sequence to find a pattern. Then generalize in terms of n.

a2 - a1 = 875,00 - 937.50 = -62.50
a3 - a2 = 812.50 - 875.00 = -62.50
a4 - a3 = 750.00 - 812.50 = - 62.50
a5 - a4 = 687.50 - 750.00 = -62.50

\[a _{n} - (a _{n} - 1)\] = -62.50

Find an explicit formula.

\[a _{n}\] = 937.5- 62.50

Evaluate the form for n = 12.
an = 937.5 -62.5n
a12 = 937.5 - 62.5(12)
= 187.5
You still owe him $187.50 at the end of one year.

Answer 10

u have missed something.....

Answer 11

937.5 is the amount u owed him at the end of the first month...

since he pays 62.5 per month

at the end of the first month means he have already payed the amount of 62.5

so the total value he borrowed is 937.5 + 62.5 = 1000

and he clears this amount by paying 62.5 per month

he got 12 months

he will pay an amount of 12 * 62.5 = 750 by the end of the year

so the amount he owe at the end of the year is 250

:D

Answer 12

got it :) ?

Answer 13

Oooh okay I think that makes sense.

Answer 14

Thank you!!

Answer 15

u r welcome !

Answer 16

Actually, the distinction is unimportant here — you only need to find how many more payments will be made by the end of the year (7) and multiply by the payment amount ($62.50) and subtract that quantity from the last reported owed amount.

Answer 17

yes ... i agree with u whpalmer.... but i solve it that way so rushal can understand his mistake while sarah can understand the problem.... :)

Answer 18

Yep. No complaints there!

Answer 19

kk :)