Question

anyone knoews financial algebra ?

Answer 1

algebra is algebra ... whats the question?

Answer 2

balloon mortgage... i have no idea how to do this...

Joanne and Bill are financing $305,500 to purchase a house. They obtained a 20/6 balloon mortgage at 5.75%. What will their balloon payment be?

Answer 3

if i just can get the steps to get the answer on at least one i will be able to do the rest... i think.

Answer 4

can you tell me the definition of a 20/6 term?

Answer 5

20/6 refers to the terms of the mortgage. The 20 means that the beginning fixed monthly payments are going to be calculated as if
the mortgage would be paid off in 20 years. The 6 means that fixed payments will be made for 6 years. After the 6 years, the balloon payment is due.

Answer 6

ok, so we want to calculate the payments on a 20 years 5.75 loan and annuity it for 6 years

Answer 7

i believe so.

Answer 8

monthly payments, or yearly payments?

Answer 9

yearly because my answer choices are too high to be monthly.

Answer 10

\[B = -P(\frac{1-k^n}{1-k})\]
then let n=20, and k = 1.0575; B = 305500
\[305500=-P(\frac{1-1.0575^{20}}{.0575})\]
\[-305500(\frac{.0575}{1-1.0575^{20}})=P\]
seems about right for that part

Answer 11

assuming our payment is due at the end of a year, and not during the months of the year, that gets us $8531 each year

Answer 12

ugh, that doesnt sound right for some reason :/

Answer 13

thats the formula they gave me ...

Answer 14

thats about right to me, they are using n as the yearly compuonding factor, and t as years then

Answer 15

idk where the numbers go though :(

Answer 16

M is the monthly payment amount.
P is the principal.
n is the number of times interest is compounded each year.
t is the number of years used to calculate the monthly payments.
r is the interest rate in decimal form.

Answer 17

yeah, thats the line up all right

Answer 18

M = 305500((.0575(1+(.0575/12)^(12*20))/12)/((1+(.0575/12))^(12*20)-1))

http://www.wolframalpha.com/input/?i=305500%28%28.0575%281%2B%28.0575%2F12%29%5E%2812*20%29%29%2F12%29%2F%28%281%2B%28.0575%2F12%29%29%5E%2812*20%29-1%29%29

gets us about 681 a month

Answer 19

http://www.wolframalpha.com/input/?i=305500%281-%281%2B.0575%2F12%29%29%2F%281-%281%2B.0575%2F12%29%5E%2812*20%29%29

my formula is alot easier to read tho

\[M=P(\frac{1-k}{1-k^{nt}})\]
let k=1+(r/n)

Answer 20

would you say the balloon payment is whats left to pay off the loan? or is it what left to pay off if we would have made all the payments for 20 years?

Answer 21

20 - 6 = 14 years of payments; so its either M(12*14)

or, its just the amount left to pay off the balance of the loan: 305500 - M(12*6)

Answer 22

\[M_0=B\]
\[M_1=B(k)-P(1)\]
\[M_2=B(k)^2-P(1+k)\]
\[M_3=B(k)^3-P(1+k+k^2)\]
...
\[M_n=B(k)^n-P(\frac{1-k^n}{1-k})\]
when \(M_n=0\) we have paid off the loan with interest
\[0=B(k)^n-P(\frac{1-k^n}{1-k})\]
\[B(k)^n=P(\frac{1-k^n}{1-k})\]
\[B(k)^n(\frac{1-k}{1-k^n})=P\]
let k=1+.0575/12, and let n=12*20
305500(1+.0575/12)^{240}(.0575/12)/(1-(1+.0575/12)^240)

gives us a more realistic approach to this; monthly payments of $2144.87

Answer 23

2144.87*12*14 = 360,338.16

if its the other way then

305500-2144.87*12*6 = 151069.36

Answer 24

i went over this all last ight @amistre64 and the answer you got isnt one of my choice :/ i'm sort of lost