Help with Algebra II word problems?

Question

Dung Nguyen is considering refinancing his home at a lower interest rate. He has an 11.875% mortgage, is presently making mo nthly principal and interest payments of $510, and has 20 years left on his mortgage. B/C interest rates have dropped, CMC is offering him a rate of 9.5% which would result in principal and interst payments of $420.50 for 20yrs. However, to get this mortgage, his closing cost would be $2500.00
A) How many months after refinacning would he spend the same amount on his new mortgage plus closing cost as he would have spent on the original mortgage?
B) If he plans to spend the next 20 years in the house, would he save money by refinancing?

Answer 1

A Let x equal no of months to spend the same amount under each deal.
then 510 x = 420.50 x +2500
89.50 x = 2500
x = 2500 / 89.50 = 27.93.. or 28 months

B No further calculation is necessary. After 28 months he is ahead by 89.50 every month so
YES is the answer from the result of A.

Answer 2

this is not as hard as it looks
they throw in those interest rates but they are not relevant to the problem

let n= number of months after refinance opportunity

with the old mortgage, his costs n months later is
n*510

with the new mortgage, his cost is
n*420.50+2500

these are equal when

510n=420.5n+2500
89.5n=2500
n=27.93

so, at approximately 28 months (2 years 4 months), Dung here will have paid off his 2500 closing cost with the savings from his lower monthly payments

every month after that he will be pocketing the 89.50 a month savings

so, yea, he would save money

this solution neglects the time value on the $2500 that had to be put up for 28 months, but taking that into consideration wouldn't change the answer much

Answer 3

For all word problems, use a variable for the thing you are looking for. Use M for months. The original mortgage is 510M and the new one +closing costs is 420.50M+2500. Put these in the inequality described and solve for M. If this isn't enough help, ask a more specific question by editing your question.

(I assume algebra II ignores the time value of money)

Answer 4

$510 x 20 x 12 =$122400 this is the cost of the existing loan over 20 years. $420.5 x 20 x 12 + $2500 = $103420 this is the cost of the new loan so:
B) Yes he would save money.
A) 510m = 420.5m +2500
510 = 420.5 +2500/m
89.5=2500/m
m=2500/89.5 where m is months to break even

Answer 5

12 lbs. of meat and and cheese adds up to $64.24. 4.95 for ham 6.99 for turkey 7.99 for roast 4.36 for cheese How many pounds of each. Add all the meat up , so 'm roughing it out out to $ 30 for cheese and $34 for the meat.