Question

You are interested in buying a new home that costs $280,000. The mortgage company requires a down payment of 15% of the cost of the home. You will borrow the rest. The mortgage company offers you 2 options. Option 1 is a 15 year loan with an APR of 6.75% and option 2 is a 30 year loan with an APR of 5.55%.

a. For each option, find the monthly mortgage payment, the total amount paid back and the total amount of interest paid. Write these in your Word document.

b. Which option would you choose and why?

Answer 1

help

Answer 2

Step one is to find out what that down payment is.

Answer 3

42,000

Answer 4

residual amount is 238,000

Answer 5

Alright, next: it's talking about monthly payments, so find out how many months 15 years is and how many months 30 years is.

Answer 6

Also, you'll want to divide you APR (annual percentage rate) by 12 to get the monthly rate.

Answer 7

180 months and 360 months

Answer 8

what would be the next step im so lost

Answer 9

0.005625
and
0.004625

Answer 10

now what @cliffsedge

Answer 11

Have you worked with exponential functions before?
(Is this an algebra 2 class, or some other kind of course?)

Answer 12

algebra

Answer 13

college algebra

Answer 14

i really needa get this done in the next 10 minutes =(

Answer 15

Ok, so you have probably seen an exponential function before, something like \(\large y=a\cdot b^{kx}\)

Answer 16

yes i have

Answer 17

im staring so hard at my screen for an answer

Answer 18

Great, so in this situation, the x in the exponent is the time (the number of months.
The compound interest formula is
\[A=P(1+R)^t\]
A is the amount after t months,
P is the 'principal' (the initial amount)
R is the interest rate (in this case adjusted to be per month.)

Answer 19

i did this but the number is soooo high i don't think its the answer

Answer 20

If you're staring at the screen for an answer, you're looking in the wrong place. You need to be looking in your own brain for that.
I can help you use what you already know to find it, but you have to do the work yourself.

Answer 21

this is what i got

Answer 22

42000*(1+.0675)^15 = 111883.887

Answer 23

but isnt the formula P=(1+R/n)^n*T

Answer 24

@cliffsedge

Answer 25

It depends on what you are using for R. If you are using the APR as R, then yes, you need to divide by n (the number of payment periods) to adjust the annual rate to whatever other time period you are using (in this case, months, so n=12 periods per year).

Answer 26

isnt it APR in this case

Answer 27

I usually prefer to make the time period adjustments first and get a new, adjusted R, so the formula is a little easier to use.

Answer 28

ok so whats the next step

Answer 29

Yes, you may use R= APR, then you need to divide by n to adjust the rate, and multiply t by n to adjust the time.
Like I said, I prefer to make the adjustments to the rate and the time first before putting things into the formula just to simplify the look of the formula. Either way will work out the same.

Answer 30

ok sounds good

Answer 31

I think (and I might be missing something because it's been a decade or so since I've worked in financial accounting, but I think all you need to do is use that formula to find out what the total amount will be after however many years, then divide by that many months to get the monthly payment.

Answer 32

wait
dont go anywhere let me do it real fast

Answer 33

There are formulas coming to mind from my engineering economics class that make me think there is something else you need to do, but it's been nearly ten years since I've studied that in detail as well.

Answer 34

i got 634008.6929

Answer 35

I recommend you get a second opinion. I can check your algebra and make sure you're solving the equations right, but if there is a nuance to how the finances work that I'm missing, then I might lead you astray.

Answer 36

That value seems a little high, but I'll check it; hold on....

Answer 37

please helpppp

Answer 38

For the 15 year, 6.75% loan, I got a total amount of $653,232.85
So, you answer is in the right area . . . how did you get it?

Answer 39

i used the formula u gave me

Answer 40

wait but ok u have to pay that much off to fullfill repayment? from a 238,000 loan?

Answer 41

At nearly 7% per year for 15 years, ... yeah, that interest adds up.
However, from my experience with this sort of thing, I know that that only gives an estimate because if you make a payment each month, then the interest rate is applied to the balance that you owe after making the payment.

Answer 42

ok so u got that answer for the 15 years? can u tell me how u got that whic formula u used cuz i cant seem to come up with that answer

Answer 43

Sure. The 6.75% APR is 0.005625 on a monthly basis.
15 years = 180 months.

\(\large A=238,000(1.005625)^{180}\)

Answer 44

waitttt where did u get that .005625 from

Answer 45

it takes forever for a reply

Answer 46

omfg i coulda been done by now

Answer 47

this is one friggin problem omfg..........

Answer 48

hero do u kno how to do this

Answer 49

?

Answer 50

@agent_sniffles

Answer 51

Okay, I'll post the steps

Answer 52

Down Payment
= .15(280,000)
= 42,000

Borrow Amount:
= 280,000 - 42000
= 238,000

Option 1:
A = 238000(1.0675)^15
A = 634,009

Option 2:
A = 238000(1.0555)^30
A = 1, 203,160

I would choose option 1 because it costs less. Better to get it over with and pay less than to pay more over a longer period.

Answer 53

hmmmmmmmmmmm i got exactly that

Answer 54

but what about everything else? how do i get the mortgage payment?

Answer 55

For each option, find the monthly mortgage payment, the total amount paid back and the total amount of interest paid

Answer 56

monthly mortgage payment do i just divide by how many months 15 years equals to?

Answer 57

I didn't compute monthly mortgage amount. Looks like cliffsedge got that covered.

Answer 58

i dont understand how he does it please explain to me hero my hero

Answer 59

Does there appear to be anything I missed for getting the monthly amount, @Hero ?
The last course I took which covered this was Engineering Economics, and it was quite complicated, so I might be over-thinking things in that mode. Since then, I've only ever used exponentials to pay off my credit cards, so maybe mortgages are different?

Answer 60

He converted APR and number of years to monthly payments.

15 years = 180 months
6.75/12 = .5675

Answer 61

Which is the correct approach. If you use that you get:
A = 238000(1.005675)^180
A = 653,233

Answer 62

ohhhhhhh ok i see now

Answer 63

but what is that number is that the total amount paid back that you just found?

Answer 64

I'm not really sure how to find the monthly payment. But there are calculators that you can use.

Answer 65

wait but what did you just figure out though how does that differ from the first one of 634,009

Answer 66

2106.08

I get that for monthly payments using the calculator.

Answer 67

can you tell me how you got that?

Answer 68

Use this:
http://www.bankrate.com/calculators/mortgages/mortgage-calculator.aspx?MSA=2120

Answer 69

^ Heh, I used to work for bankrate.com for like three years. I was an accountant there.
I've forgotten how to do all this stuff since then. :">

Answer 70

Sorry I couldn't be more helpful.

Answer 71

how do u forget if u worked doing this kind of stuff

Answer 72

i got 2477.75

Answer 73

wait but what is this though 653,233 how does that differ from the first one of 634,009

Answer 74

Don't pay attention to the 634,009. It was computed using the annual percentage rate rather than monthly percentage rate.

Answer 75

@yomamabf "how do u forget if u worked doing this kind of stuff "

It was over 15 years ago, and I've been doing physics and engineering since then, so my mind has been immersed in other equations since.

Sorry, but the human brain can only remember so many things over time.

I guess I should have studied more. :-p

Answer 76

Yeah, it is easier to document course work you have done over a period of time rather than try to remember it all. That way, you can refer to it later as reference material.

Answer 77

@hero um hello?wait but what is this though 653,233 how does that differ from the first one of 634,009

Answer 78

help me satelliteeeeeeeeeeee

Answer 79

i hate to throw cold water on this, but i don't think those are the right payment formulas

Answer 80

oh sorry, i missed @hero link let me shut up

Answer 81

you have to borrow 85% of 280,000 which is 238,000
use the mortgage calculator link hero sent

Answer 82

15 years at 6.75 gives a monthly payment of $2106.08

Answer 83

30 years at 5.55 gives a monthly payment of $1358.81

Answer 84

total payment over 15 years is \(180\times 2106.08= 379,094.40\)
and total payment for 30 years is
\(360\times 1358.81=489,171.60\)

Answer 85

you pay a lot more over the course of the loan with the 30 year mortgage, on the other hand maybe you cannot afford such high monthly payments that the 15 year mortgage has
besides, maybe you will move in 5 years

Answer 86

thank you satellite73 god of math! *bows*

Answer 87

Yeah, but @satellite didn't explain how to find the monthly payment without using the link.

Answer 88

way to steal his shine kanye west

Answer 89

i can do that if you like, but it is boring

Answer 90

\[pmt=\frac{P\times \frac{apr}{12}}{1-(1+\frac{apr}{12})^{-12Y}}\]

Answer 91

I wasn't trying to steal anyone's shine

Answer 92

I was just stating the obvious.

Answer 93

assuming monthly payments
borrowing P dollars
at apr written as a decimal for Y years

Answer 94

@satellite, Did you derive that formula yourself or did you find it in a book?