Expert: Sherry Wallin - 1/26/2009

Question
QUESTION: HI, im having trouble with a question ive tried it but im not sure if i did it right.Can you please check and correct me if im wrong.
this was the information given and the questions are after this table.

Debt          Interest Rate    Principal Remaining
Mortgage    7.5 % Compounded Monthly     $170,000
Mara’s Car Loan 4 % Compounded Monthly   $15,500
Joe’s Student Loan 5 % Compounded Monthly $12,000
Joe’s Visa     18 % Compounded Monthly    $3500
Mara’s Visa    22 % Compounded Monthly    $1500
Mara’s MasterCard 18 % Compounded Monthly  $1100
Joe’sFutureShopCredit Card 28 % Compounded Monthly  $800

They make a mortgage payment every month and have 15 years of payments remaining. They make Mara’s car payments every month as well and have 48 months remaining. Because it is time to renegotiate their mortgage, the bank has provided them with two options:
1) Combine the remaining principals of all their debts into a new 15 year mortgage with monthly payments at 8% compounded monthly.
2) Refinance their mortgage (for a term of 15 years with monthly payments) with interest at 7.5% compounded monthly, and consolidate the principals of all their remaining debts into a 5 year loan with monthly payments and interest at 9% compounded monthly.
a) What are the monthly payments under option 1? What is the sum of all their payments?
b) What are the monthly payments under option 2? What is the sum of all their payments?
c) Which option would you choose?

my solution was
A/ pv=r(1-(1+r/i)^-n)/i
  18900=r(1-(1+0.0067)^-180)/0.0067
  18900=r(104.39)
  181.1=r

B) 170000=r(1-(1+0.00625)^-180)/0.00625
  170000=r(167.87)
  1575.97=r

34400=r(1-(1+0.0075)^-60)/0.0075
34400=r(48.17)
714.14=r

ANSWER: Hi Ashwathi~
   I see you've asked me to check your answers but the questions are the sums and monthly payments and all I see are values for r which is given in all the parts of the problems. Typically r stands for the interest rate and the r in both parts of A is the same r (you can't use a variable twice in the same problem to mean different things). I can give you the answers and I will but I fear this is not all you are looking for. Please be more specific with what you want from me and label your variables clearly.

a) the monthly payment would be  $1953.35 and the sum of the payments is $351,603

b) the monthly mortgage payment is $1575.92 and the sum off the payments is $283,665.60

the monthly payment on the remaining debt is $714.09 and the sum of the payments is $42,845.40

sum of all payments part b is $283,665.60 + $42,845.40 = $326,511

Although you would be paying out $336.76 more per month for the first 60 months (of 180 months) you would save over all $25,092, this would lead me to believe I would choose option b if I had the monthly income to cover the larger payment.

---------- FOLLOW-UP ----------

QUESTION: im sorry if i was not clear, i wanted to know what equation i was supposed to use, for each part of the question. How did you come up with that answer? can you please tell me which equation im supposed to use and how to plug in the numbers. althought i did get 714.14 and 1575.9 in my solutions above. also i have a doubt about the sum of all payments? how did you get the sum? id be thankful if you explained this to me.

Answer
To get the sum of all the payments just multiply the payment by the number of months you are going to make the payment. For the $204,400, (all debt consolidated) multiply the payment 1953.35 by 180 and for the mortgage only multiply 1575.92 by 180 and multiply the other debt payment 714.09 by 60 and add them together.

I do see you have the values 714.14 and 1575.9 in your solutions but you have them labeled r which is the interest rate as I said above. It appears the formula you used is the correct one to calculate the monthly payments. For part A use the same formula as you used in part B:
only label it differently like A for amount thus
204,400 = A(1-(1+.08/12))^-180/(.08/12)
note .08/12 = .0067 so
204,400 = A(1-(1+.006666666 ))^-180/(.006666666)
= A(1-.302396088)/.006666666
= A(.697603912)/.006666666
= A(104.6405972) --> A = 1953.35 so this is the payment and multiply it by 180 and you will get the sum 351,603

Math Prof