Question

Mat obtains a mortgage for $250,000 with the following terms:

- 15 year 5/1 ARM at 6.5% with a 3/7 cap structure
- - Initial monthly payments: $2,177.77

What will be the balance of the loan at the end of the initial interest rate period?

I got 191,792.80

Answer 1

the key here is understanding the 5/1 notation. what do you recall?

Answer 2

and if you have covered balloon payments, thats basically what its asking

Answer 3

250000k^(5*12) - 2177.77(1-k^(5*12))/(1-k). k=(1+.065/12)

http://www.wolframalpha.com/input/?i=250000k%5E%285*12%29+-+2177.77%281-k%5E%285*12%29%29%2F%281-k%29%2C+k%3D%281%2B.065%2F12%29

191 793 is fine

Answer 4

Thank you. Can you check a couple more?

Answer 5

if my sanity holds out sure :)

Answer 6

Hahah cool, thank you.

Answer 7

Marie has a 20 year adjustable rate mortgage with a fixed rate for the first 7 years. In the 8th year, the interest rate rises to 6.2%. the remaining balance at the end of the 7th years is $398,381.20. What is the monthly payment in the 8th year?

I got 2553.73

Answer 8

so we pretty much want to take out a loan for the remaining balance for the remaining time period at the adjusted rate .... correct?

Answer 9

Bk^n(1-k)/(1-k^n) = P

398,381.20(1+.062/12)^(12(20-7))(1-(1+.062/12))/(1-(1+.062/12)^(12(20-7)))

http://www.wolframalpha.com/input/?i=398%2C381.20%281%2B.062%2F12%29%5E%2812%2820-7%29%29%281-%281%2B.062%2F12%29%29%2F%281-%281%2B.062%2F12%29%5E%2812%2820-7%29%29%29

im getting something else, did you use the adjusted time frame? 20 - 7

Answer 10

Hmm okay is it 177711.51?

Answer 11

show me you work if you can

Answer 12

you are most likely using a formula, what is your formula?

Answer 13

and are there options?

Answer 14

i use my own formula that i develped during the class simply becuase it is sooo useful in so many applications instead of trying to recall all the other formulas for each situation.

Answer 15

a little workings .. we have a balance B, that gets interest ,r, added to it and then a payment ,P, removed:

Bo = B
B1 = Bo(1+r) - P
B2 = B1(1+r) - P = Bo(1+r)^2 - P(1+r) - P
B3 = B2(1+r) - P = Bo(1+r)^3 - P(1+r)^2 - P(1+r) - P

.... let k clean up the compounding rate stuff to read easier

Bn = Bok^n -P(1+k+k^2+...+k^(n-1))

since P represents a geometric series ...

Bn = Bok^n - P(1-k^n)/(1-k)

and thats the formula i use

Answer 16

The other options are 119333.90 and 234027.44

Answer 17

to determine monthly payment, then when Bn = 0, for n periods

P = Bo k^n(1-k)/(1-k^n)

n=12(20-7)
k=1+.062/12
Bo = 398381.20

Answer 18

Okay so 234027.44?

Answer 19

im getting 3725.90

Answer 20

Wait, I was looking at a different question! Oh man im sorry I gave the wrong options. but now it makes sense. Im so sorry

Answer 21

youre options arent making any sense, ... :)

Answer 22

Haha I know I see that too haha.

Answer 23

Can you check a couple more?

Answer 24

has this one been satisfied? we had different solutions, do we know why?

Answer 25

Haha yes we do haha. Again im sorry for the different ones.

Answer 26

lets do another then

Answer 27

..... testing my sanity i spose lol

Answer 28

Hahah thank you :)

Answer 29

An investor obtains a balloon mortgage with the terms shown below:

$370,00
20/5 balloon
5.1 % annual rate

What is the monthly payment on this mortgage?

I got $2,184.59

Answer 30

monthly payment is the same as a 20 year fixed rate loan

P = Bo k^n (1-k)/(1-k^n)

P = 370000 k^(12*20) (1-k)/(1-k^(12*20)), k=(1+.051/12)

P=2462.32 it would be helpful to know how you are approaching your solutions

Answer 31

This one I guessed, but how did you get 2462.32?

Answer 32

i posted how i got the formula i use and then just used the formula ...

Answer 33

what are the options if any?

Answer 34

The other ones are 6999.32, 6481.17, 2462.32, and the first one I did.

Answer 35

id go with 2462 then :)

Answer 36

theres a monthly payment formula in your course materials, my own formula is an unsimplified version of it that just makes more sense to me personally

Answer 37

Oh okay cool then :) They should teach your formula. I have another question that is similar.

Answer 38

lets try it out

Answer 39

Balloon Mortgage: $300,000
25/5 balloon
6% annual rate
Initial Monthly Payment $1932.90
What is the amount of the balloon payment rounded to the nearest dollar?

I got $271,145

Answer 40

Or is it $280,559?

Answer 41

so the remaining balance after 5 years of payments, 5*12 = 60 payment periods

B60 = Bo k^(60) -P(1-k^(60))/(1-k)

B60 = 300000 k^(60) -1932.90(1-k^(60))/(1-k), k=1+.06/12

http://www.wolframalpha.com/input/?i=300000+k%5E%2860%29+-1932.90%281-k%5E%2860%29%29%2F%281-k%29%2C+k%3D1%2B.06%2F12

about 269 797 is what i get

Answer 42

That's one of the choices. How come its not 271145?