Question

Stuck on this business problem. Help. xoxo

Rush Trainer purchased a houseboat for $165,000. The financing company requires a 15% down payment for a 30-year loan at 7%. At the end of 30 years, what will be the total amount of interest charged? (Hint: First subtract the down payment from the purchase price to find the amount to be financed.)
http://imgur.com/ZRjfV86

Answer 1

i'll see what i can do

Answer 2

Thank you homie

Answer 3

Did you subtract it yet?

Answer 4

165,000*0.15=24,750
165,000-24,750=140,250
Ok there.

Answer 5

What next?

Answer 6

now we need to look at the table

Answer 7

find the monthly payment

Answer 8

6.65

Answer 9

7% 30 year loan has a 6.65 monthly payment for a 1000 dollar loan. now lets scale this loan . how many thousand dollars is in that loan

Answer 10

Do i multiply that by 1000?

Answer 11

140250 / 1000

Answer 12

we can make a proportion

Answer 13

Actually don't I do this?
\[\frac{ 165,000 }{ 1,000 }*6.65=1,09\]

Answer 14

$$

\Large \frac{6.65}{1000} = \frac{x} {140,250}

$$

Answer 15

oh wait, why 140,250??

Answer 16

that is the actual loan. the table has a list for a 1000 dollar loan

Answer 17

we want to calculate the monthly payment. so we are scaling up the payment for 1000 dollar loan up to a 140,250 loan

Answer 18

Ohhh ok, so basically
165,000*.15=24,750
165,000-24,750=140,250. I gotcha. Thanks. Continue please.

Answer 19

$$
\Large { interest = total paid - amount~ loaned
\\
= 932.66 * 30yrs*12months - 140,250

}
$$

Answer 20

$195,507.60

Answer 21

one sec im checking this over

Answer 22

Ok the way you did it was different than the formula my school provided. You set up the proportion differently. Maybe they didn't give me the correct formula. Let me check my answer real quick.

Answer 23

Yup, it said it's incorrect :p

Answer 24

why 93?

Answer 25

https://www.google.com/search?q=monthly+loan+calculator&ie=utf-8&oe=utf-8

Answer 26

473?

Answer 27

ok so look at the table and look at 30 (length in loans in years) on the x axis and the 7% on the y axis. that will give you 6.65

Answer 28

hmm, actually it seems to come out the same
932.66 ~ 933

Answer 29

ok we did it right there was rounding error

Answer 30

hmm, ok i see what youre getting at

Answer 31

so the idea to make a proportion does work . but your computer have a slight difference in actual number

Answer 32

are we supposed to use a table. if so then
$$
\Large \frac{$6.65 mth~ payment}{$1000~ loan} = \frac{x~actual ~mth ~payment} {140,250~ actual~loan}

$$

Answer 33

this is true for a 30 year, 7% loan

Answer 34

compounded monthly

Answer 35

so that means 933? or 932.66.
Do i have to round?

Answer 36

well you told me your computer doesn't like the first answer

Answer 37

nope, it said its wrong. I think its probably the school system...

Answer 38

lets try the rounded answer, one moment

Answer 39

can you take a screenshot of the error

Answer 40

okay. thank you

Answer 41

im on a mac. i dont know how to screenshot. give me one second.,

Answer 42

according to this calculator the interest is :
$195,661.23

Answer 43

http://www.thecalculatorsite.com/finance/calculators/loancalculator.php

Answer 44

Hm, well it doesnt let me screenshot. but i put that answer too and it says its incorrect...

Answer 45

and $
195508.50 is wrong?

Answer 46

Yaay thats the right answer :D

Answer 47

oh my calculation was correct

Answer 48

Nope, its because i but $195,50(7).50. on accident. Im sorry!

Answer 49

Ahh, i feel bad. sorry for my miscalculation and thank you for you time perl :)

Answer 50

Okie dokie, have a good day. thank you once again.

Answer 51

$$
\Large {\frac{$6.65 mth~ payment}{$1000~ loan} = \frac{x} {140,250 actual~loan}
\\ \iff \\}

\Large {
{6.65} \cdot {140250} = {x}\cdot {1000}\\
\\ \iff \\
\frac{{6.65} \cdot {140250}}{1000}= x \\
\\ \iff \\
~monthly ~ payment =x=932.66
\\ \iff \\
}

\Large {interest\\ = total paid - amount~ loaned
\\= monthly~payment \cdot \# yrs \cdot \# months - principal

\\
\\ \therefore \\
interest = 932.66 * 30yrs*12months - 140,250 \\
~~~~~~~~~~~~~~=$195508.50
}


$$

Answer 52

interesting that the interest itself is worth more than the original loan . so thats a giant cost for a loan. but its spent over 30 years so the feeling is assuaged by time

Answer 53

Thank you perl, this really helps me understand :)