Comments on: mortgage math problem: Between her home mortgage, car loan, and credit card bill, Megan is $75,300 in debt?

By: Ja Ma

Ja Ma — Sun, 02 Nov 2008 08:09:54 +0000

d=credit card loan, c=car loan, m=mortgage
total monthly interest expense = 0.015*d + 0.01*c + 0.006*m = 460.50
i am assuming that this amount is the monthly interest expense not the “accumulated” interest expense.
also we have that 0.015*d - 0.01*c = 4.50
we also know that megan is 75,300 in debt so,
d + c + m + 460.50 = 75,300
assuming that it is the end of the month and “in debt” includes interest obligations this month. it says “after” one mont

now we have three equations in three unknowns to solve
use the second relation to express c in terms of d
c = (0.015*d - 4.5)/0.01 or c = 1.5*d - 450

substitute into the third relation to get
d + 1.5*d - 450 + m + 460.50 = 75,300
2.5*d + m = 75,289.50
express m in terms of d
m = 75289.50 - 2.5*d

now we can write the first expression in terms of d
0.015*d + 0.01*(1.5*d-450) + 0.006*(75289.50 - 2.5*d) = 460.50
collect terms
0.015d + 0.015d -4.5 + 451.74 - 0.015d = 460.50
0.015*d = 13.26
d = 884
her credit card debt is $884
solve for c
c = 1.5*d - 450 = 1.5*884 - 450 = 876
her car loan is $876
solve for m
m = 75289.50 - 2.5*d = 75289.50 - 2.5*884 = 73,079.50
her mortgage is $73,079.50

see if it adds up
total 884 + 876 + 73079.50 + 460.50 = 75,300
voila

By: Jenna K

Jenna K — Sat, 01 Nov 2008 17:06:16 +0000

x = mortgage
y = car loan
z = credit card

x + y + z = 75,300
.006 x + .01y + .015z = 460.5
.015z - .01 y = 4.5

solve the third equation for y:
y = 1.5z - 450

Substitute for y in the first equation and solve for x:
x + 1.5z - 450 + z = 75,300
x + 2.5z = 75,750
x = 75,750 - 2.5z

Substitute for x and y in the second of the original equations and solve for z:
.006 (75,750 - 2.5z) + .01(1.5z - 450) + .015z = 460.5
454.5 - .015 z + .015 z - 4.5 + .015 z = 460.5
.015 z +450 = 460.5
.015z = 10.5
z = 700

Find x:
x = 75,750 - 2.5z
x = 75,750 - 2.5 (700)
x = 74,000

Find y:
y = 1.5z - 450
y = 1.5(700) - 450
y = 600

Check the variables in our initial equations:

74,000 + 600 + 700 = 75,300
.006 (74,000) + .01(600) + .015(700) = 460.5
.015(700) - .01(600) = 4.5

By: payjani

payjani — Sat, 01 Nov 2008 14:16:28 +0000

I found you several calculators that figure mortgages with the interest rates that you tell it to calculate this will also work for car loans just adjust the time frame in which you are paying for the car for example
5 years = 60 months
6 yrs. = 72 and so on this is a great tool to use
have fun
Janice

By: miko

miko — Fri, 31 Oct 2008 23:03:19 +0000

Glad I alReady graduated. GOOD LUCK!