Martha asked:
The monthly interest on her credit card is 1.5%, the monthly interest on her car loan is 1%, and the monthly interest on her mortgage is 0.6%. After one month, her total accumulated interest is $460.50. If the interest on Megan’s credit card bill was $4.50 more than the interest on her car loan, find the amount of each loan.
Lloyd
The monthly interest on her credit card is 1.5%, the monthly interest on her car loan is 1%, and the monthly interest on her mortgage is 0.6%. After one month, her total accumulated interest is $460.50. If the interest on Megan’s credit card bill was $4.50 more than the interest on her car loan, find the amount of each loan.
Lloyd
Tags: Car Loan, Credit Card Bill, Home Mortgage
Glad I alReady graduated. GOOD LUCK!
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
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
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