lecture 32 outstanding balance refinancing ana nora evans 403 kerchof [email protected] ans5k...

Lecture 32Outstanding

BalanceRefinancing

Ana Nora Evans 403 [email protected]://people.virginia.edu/~ans5k

Math 1140 Financial Mathematics

2Math 1140 - Financial Mathematics

The exam 2 was

A) EasyB) Just rightC) HardD) Too hard


Exam 2 Grades


Assuming you keep working on bonus problems and get a 100 on the project the grade distribution not counting the final, with 100 on the project is:


Final

The final is on December 8, 7-10pm. Location to be announced.There will be 15 problems on the final: 5 questions from chapters 1, 2, 3 5 questions from chapters 4,5 5 problems from chapters 6,7


The first 10 questions will be similar to exams 1 and 2 (questions from study guide, problems from homework or practice problems).The last 5 problems will be similar to problems from homework 11 trough the last homework.No sample exam, practice problems or study guide will be provided!For practice problems use the textbook!

Math 1140 - Financial Mathematics7


Last time

Defined what it means to amortize a debt.We calculated how much of each payment goes to the interest and how much goes to the principal.


Balance after kth payment: P(1+i)k - R s(k,i)

How much of the (k+1)th payment goes to the interest?

[P(1+i)k - R s(k,i)](1+i)

How much of the (k+1)th payment goes to the principal?

R - [P(1+i)k - R s(k,i)](1+i)


Discount Points

A point is 1% of the amount of money being lent.Discount points is an up-front charge on the amount being lent.


Alice borrows P dollars at rate i per month and p points with monthly payments for n years.

What is the real APR?

Step 1: Calculate R

Step 2: Calculate APR

Present value: (1-p)P

Rent: R

Number of payments: 12n

Discount points not added to the principal

ni

iPR

12)1(1



What is the real APR if the points are added to the loan?

Step 1: Calculate the amount borrowed

Step 2: Calculate R

Discount points added to the principal

p

PX

1

nn ipP

i

i

iXR

1212 )1(11

)1(1



What is the real APR if the points are added to the loan?

Step 3: Calculate APR

Present value: P

Rent: R

Number of payments: 12n

Discount points added to the principal


Outstanding Balance

The outstanding balance is the principal still to be paid.


Prospective Method

The outstanding balance at a given time is calculated as the sum of the remaining payments moved to the given time.Given the rent R and the number of payments left m, the outstanding balance is:

i

iR

m )1(1


What loan data we need to know to apply the prospective method?- the periodic payment- the number of remaining payments- the interest rate


Retrospective Method

The outstanding balance at a given time is the amount borrowed moved to that time minus the sum of the payments considered at the given time.Given the rent R and the number of payments n,the outstanding balance after the kth payment is

i

iRiP

kk 1)1()1(


What loan data we need to know to apply the retrospective method?- the periodic payment- the number of payments made- the amount borrowed- the interest rate


Do the prospective and retrospective give the same value of the outstanding balance?A) YesB) No


How do we decide which method to use?

A) We can use either one.

B) We always use the prospective method.

C) We always use the retrospective method.

D) The method used depends on the problem.


The two methods give the same value if no rounding is allowed.The prospective method is less accurate when all the payments are rounded to the nearest cent.


Alice takes a $85,000 loan financed at 8.5%(12) for 15 years, with monthly payments. Find the outstanding balance at the end of 8 years.

Which method should we apply?

The retrospective method.

Step 1: Calculate the monthly payment

ni

iPR

)1(1

03.837$)

12085.0

1(1

000,85$12085.0

1512

R



Step 2: Calculate the outstanding balance

i

iRiP

kk 1)1()1(

53.854,52$

12085.0

1)12085.0

1()

12

085.01(000,85$

812

812

R



Use prospective method.

The number of payments left is m=12×15-12×8=84.

The outstanding balance is:

i

iR

m )1(1

53.854,52$

12085.0

)12085.0

1(103.837$

84


Alice makes monthly payments of $900 for a 12%(12) loan. If she has 10 years left on the loan, what is the outstanding balance on the loan?

Which method should we use to calculate the outstanding balance?

A) Retrospective

B) Prospective

C) Either


Refinancing a Loan

Refinancing a loan means to take out a new loan to pay off the existing loan.Why would anyone want to do it? To get a lower rate. To change the term. Shorter term has higher payments. Longer term has smaller payments.


A home loan for $52,000 is financed at 8.5%(12) for 30 years and no points.

Find the interest saved if this loan is refinanced at 7%(12) at the end of the 10th year, leaving the remaining term unchanged.

Step 1: Calculate the payment of the first loan

P = $52,000

i = 0.085/12

R = $399.84

3012)1(1

i

iPR




Step 2: Calculate the outstanding balance at the end of the 10th year using the prospective method

P = $52,000

i = 0.085/12

R = $399.84

k = 12×10

OB = $46,072.39




Step 3: Calculate the payment of the new loan

P = $46,072.39

i = 0.07/12

R = $357.2

2012)1(1

i

iPR




Step 4: Calculate the interest saved

The interest saved each month is the difference of the two payments.

The interest saved is

12×20 ×($399.84-$357.2).


A home loan for $52,000 is financed at 8.5%(12) for 30 years and no points. This loan is refinanced at 7%(12) at the end of the 10th year, leaving the remaining term unchanged.

How much interest was paid during the 8.5% loan?

The interest is calculated as the difference of the sum of all payments and the amount actually borrowed:

120×$399.84-($52,000 - $46,072)


A home loan for $52,000 is financed at 8.5%(12) for 30 years and no points. This loan is refinanced at 7%(12) at the end of the 10th year, leaving the remaining term unchanged.

How much interest was paid during the 7% loan?

The interest is calculated as the difference of the sum of all payments and the amount actually borrowed:

12×20×$357.2 -$46,072


Wednesday

Read sections 6.3 and 6.4

Nov 11 (next Friday)

Project Progress Report

Dec 8 (a little over a month)

FINAL!!!!

Charge

lecture 32 outstanding balance refinancing ana nora evans 403 kerchof [email protected] ans5k...

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