Bill and terry are considering buying a house and need to figure out what they can afford and what a bank will lend them. their adjusted gross income is $166,988. their monthly mortgage payment for the house they want would be $1,544. their annual property taxes would be $9,888, and the homeowner's insurance premium would cost them $1,007 per year. they have $510 per month car loan, and their average monthly credit card bill is $5,100. would the bank lend them $210,000 to purchase their house? explain with work.

No, he bank will not lend them the loan of $210,000 because the back end ratio of Bill and terry is greater than 36% i.e. 58%. and bank only lend money to those who have back end ratio less than 36%

Step-by-step explanation:

The bank will lend them money if their back end ratio is less than 36 %

back end ratio= Total Monthly expense / Monthly gross income

in the question we have yearly insurance, so convert it into monthly cost i.e

Monthly insurance = $1007 / 12

                               = $ 83.91 =~ 84

similarly the property tax is also given yearly, convert them into monthly

Monthly property tax =  $9,888 / 12

                                   = $ 824

Now,

Total Monthly expense = monthly mortgage payment + Monthly property tax + Monthly insurance + Monthly car loan + monthly credit card bill

                                      = $1,544 +  $ 824  + $ 84 + + $510 + $5,100

                                      = $ 8062

Monthly gross income = $166,988 / 12

                                     = $ 13916

back end ratio= Total Monthly expense / Monthly gross income

                        = $ 8062 / $ 13916

                        = 0.579 =0.58

So, Bill and terry back end ratio is: 0.58 *100 = 58%

The back end ratio of Bill and terry is greater than 36% i.e. 58% so the bank will not lend them the loan of $210,000.