Question

Alexa is closing on a house on October 12. The buyer owns the property on the day of the closing. The selling price of the home is $300,200. Alexa was accepted for a 30-year fixed-rate mortgage for $278,200 at 4.75% interest. The seller has paid $3,833.62 in property taxes for the coming year. How much will Alexa owe in prorated taxes and interest?

$2,982.00
$724.00
$850.50
$1,574.50

Answer 1

@jim_thompson5910

Answer 2

one sec

Answer 3

take your time

Answer 4

so Alexa is the new owner? right?

or is she the seller?

Answer 5

the owner i think

Answer 6

hmm ok, yeah that makes sense because she gets the mortgage

ok still thinking

Answer 7

well the owner (the previous owner) paid "$3,833.62 in property taxes for the coming year"

however, the owner has only lived in the house from Jan 1 to Oct 11 of that year. The rest of the year, from Oct 12 onto Dec 31, Alexa is now living there.

Agreed?

Answer 8

yes

Answer 9

how many days are there from Jan 1 to Oct 11

Answer 10

depends if its a leap year haha

Answer 11

let's assume 365 days (non leap year)

Answer 12

you can use a calendar or use wolfram alpha to get the answer to that question

type in "Jan 1 to Oct 11" into wolfram

Answer 13

283 days

Answer 14

add one to that because they don't include Jan 1 itself

so 284 days

Answer 15

how many days are from Oct 12 to Dec 31

Answer 16

80 days not including oct 12 so 81

Answer 17

notice how 284+81 = 365, so that checks out

Answer 18

right

Answer 19

so the old owner owned the house for only 284 days out of 365 days

284/365 = 0.77808

the old owner has lived there about 77.8% of the year

Answer 20

and she has lived there for 22.2% right?

Answer 21

so it's only fair to have the old owner pay only 77.8% of the taxes

the new owner (Alexa) would pay the remainder

Answer 22

yes roughly

Answer 23

how much in taxes would Alexa have to pay for that year?

Answer 24

i know i probably sound stupid but i have no idea :(

Answer 25

would i do the 22% of the3,833.62

Answer 26

oh okay i got it so it's c?

Answer 27

that's just taxes though, we haven't considered interest

Answer 28

oh true.

Answer 29

hmm one sec

Answer 30

do you know how to find the monthly payment for the mortgage?

Answer 31

yes is it the p=i(1+i)^nt / (1+i)^nt -1 ??

Answer 32

that sounds right, so what monthly payment do you get

Answer 33

would it be compounding annually or monthly?

Answer 34

monthly I think

Answer 35

$1451.22

Answer 36

the mortgage has an interest rate of 4.75%

divide this by 12 to get ???

Answer 37

.0039583

Answer 38

now multiply that by the monthly payment and you get ???

Answer 39

5.74

Answer 40

is that right?

Answer 41

hmm that seems so very low

Answer 42

maybe I messed up and maybe it's 4.75% of the payment

Answer 43

68.92

Answer 44

the rest of that is the principal which pays off the mortgage

so we will have a balance of 278,200 - 68.92 = 278,131.08 at the end of Oct (after Alexa makes that monthly mortgage payment)

Answer 45

so do i calculate the interest of the balance?

Answer 46

yes what is the interest payment for the month of Nov

Answer 47

after we figure this out i have another question up and i have the answer to it and how i got it could you tell me if i did it right? if not its okay.

Answer 48

sure, but let's figure this one out

Answer 49

1099.82?

Answer 50

i used an amortization table so that may be wrong.

Answer 51

no, the monthly payment stays the same

Answer 52

$1451.22 is the monthly payment throughout the entire mortgage

Answer 53

oh okay.

Answer 54

so we are calculating the monthly interest amount?

Answer 55

hmm oh wait, I know what I did wrong

Answer 56

you take 0.0475/12 = .0039583

multiply that with the remaining balance (which is originally the entire mortgage)

Answer 57

sorry we'll have to back up and redo the interest amount for Oct

Answer 58

thats okay! so .0039583 x 278200 =1101.21

Answer 59

that's your interest payment for Oct

Answer 60

the remaining balance is the $278,200 - $1,101.21 = ??

Answer 61

then for november it is .0039583 x remaining balance of 277098.79= 1096.85

Answer 62

do i do december too?

Answer 63

that's the interest payment for Nov

Answer 64

yes til the end of the year

Answer 65

276001.50 x .0039583 = 1092.51

Answer 66

ok so we know this

taxes: 851.06364

Interest owed in Oct: 1101.21

Interest owed in Nov: 1096.85

Interest owed in Dec: 1092.51

Answer 67

right

Answer 68

the problem is that when we add them up, they go over the answer choices

Answer 69

hmm not sure what went wrong

Answer 70

i dunno. :/

Answer 71

oh wait, I'm not thinking lol

Answer 72

the interest for Nov and Dec isn't owed until those months come up

Answer 73

but the interest for Oct is split up

so we split 1101.21 up in such a way that it is fair to the buyer and seller

Answer 74

for Oct, the old owner lived in the house from Oct 1 to Oct 11

that's 12 days (11-1+1 = 12)

Alexa lives in the house from Oct 12 to Oct 31 (19 days)

so 19/31 = 0.612903

multiply that by 1101.21 to get 1101.21*0.612903 = 674.93491263


then you add this to the amount she has to pay in taxes

851.06364+674.93491263 = 1,525.99855263

it's a bit off, but this makes sense to me a bit better. So I'm thinking it's $1,574.50 and we may have made round off errors, not sure

Answer 75

thank you so much!!! you don't understand how much of a help you've been to me.

Answer 76

honestly I can't say for certain but I think it's correct. I would ask the teacher to confirm

Answer 77

i will. it's probably correct though.