Math Is Fun Forum

Monique

Member

Registered: 2007-02-17

Posts: 22

my family mortgage -

There are 4 people in my family who contribute to repayments. A, B and C contribute 60 percent of their weekly income and D contributes 25 percent of his weekly income to monthly repayments. A makes $720 per week. B earns $690 per week. C earns $820 per week.
We have taken out a $560 000 loan at 6.4% over a 30 year period.

a) what amount will I have to repay each month?

b) how much will I have to repay in total on this loan?

c) is there any way of working out how long it will take to pay off the mortgage if we increase the monthly repayments by 10% after 5 years of my 30 year loan period, and how much extra do we individually have to put in?

1) can anyone please explain in words and perhaps even diagrams how I would go about working out this solution, and
2) can anyone please show me the mathematical steps involved in answering this question?

Monique

Member

Registered: 2007-02-17

Posts: 22

Re: my family mortgage -

getting quite desperate is there anyone who can go through the above with me?? ganesh are you still around??!!

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: my family mortgage -

Is the interest compounded daily, monthly, quarterly, and what time of month for first one?
What is exact date of beginning of loan, and time until first compounding of interest?
Like if the yearly interest is 100%, then you double the amount at the end of the year.
Because say you start with a $5 loan from your brother.
Now a year later, 5 times (1 + 100%) = 5 x (1 + 1) = 5 x 2 = $10. Now you owe him $10.
But if he compounds twice a year, then you owe a little bit more.

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: my family mortgage -

Like $5 x (1 + 50%) = $5 x 1.5 = $7.50 dollars after six months, but then after six more months at a year, you owe $7.50 times (1 + 50%) = $7.50 x 1.5 = $11.25
So if your brother compounds the 100 percent interest twice a year, then you get to owe him $11.25 after a whole year.
Now if you want to pay him back each time he compounds interest, I would ask him does he add the interest just before you pay him, or after, or what??
When you know this, you subtract that amount that you pay to the amount at hand.

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igloo myrtilles fourmis

Monique

Member

Registered: 2007-02-17

Posts: 22

Re: my family mortgage -

hi John!

lets say the interest compounded quartelrly. The loan was issued 5 June 2002. can you help me go through each step from a) to d)...?

is there any way possible to post a graph here showing my repayments over this period?

Kind regards
Monique

Last edited by Monique (2007-02-26 10:26:03)

Monique

Member

Registered: 2007-02-17

Posts: 22

Re: my family mortgage -

very desperate - anyone available that can help me go through step by step with the above????

Last edited by Monique (2007-02-27 11:51:42)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: my family mortgage -

There are a lot of rules, and details, that are built into the computer program that the bank has, when they issue the load, I bet. 
Like what time of month do they compound the interest.
What time of month do you pay your monthly fee.
Which happens first and exactly how far apart.
How many times per month is the balance looked at or recalculated with interest.
There are so many possibilities, we can't get the right answer for your application unless we are very, very, lucky.
What about the last payment, will the bank work it out so the last payment is the same size as all the other payments, will they just have some weird final value based on some other information I haven't dreamt up yet.

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: my family mortgage -

I found this!!
Hope it helps!! Click on the following link to learn about your mortgage payments.
http://www.aliaterra.com/

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igloo myrtilles fourmis

Ms. Bitters

Member

Registered: 2008-07-31

Posts: 19

Re: my family mortgage -

There are 4 people in my family who contribute to repayments. A, B and C contribute 60 percent of their weekly income and D contributes 25 percent of his weekly income to monthly repayments. A makes $720 per week. B earns $690 per week. C earns $820 per week.
We have taken out a $560 000 loan at 6.4% over a 30 year period.

a) what amount will I have to repay each month?

b) how much will I have to repay in total on this loan?

c) is there any way of working out how long it will take to pay off the mortgage if we increase the monthly repayments by 10% after 5 years of my 30 year loan period, and how much extra do we individually have to put in?

1) can anyone please explain in words and perhaps even diagrams how I would go about working out this solution, and
2) can anyone please show me the mathematical steps involved in answering this question?

Assumption A. If your interest of 6.4% is compounded monthly and you wish to pay off the loan monthly, then your problem falls under the simple annuity case.  Under this scenario:

a) what amount will I have to repay each month?

This is a simple annuity problem.  Take note that
A = $560,000 (loan amount)
R = monthly payments (to be determined)
j = .064 (nominal interest rate)
m = 12 (interest period, as in monthly - which also happens to be the payment interval)
t = 30 years (term of loan)
You then solve for R in the following amortization equation:

Solving for R gives us

b) how much will I have to repay in total on this loan?

There are 360 monthly payment intervals (30 years * 12 months).
Thus, your total payments on this loan would be 360*$3,502.83 or $1,261,018.80.

c) is there any way of working out how long it will take to pay off the mortgage if we increase the monthly repayments by 10% after 5 years of my 30 year loan period

To work out how sooner you can pay off your mortgage if you increase the monthly repayments by 10% after 5 years of your 30 year loan period, you must first work out how much your outstanding loan balance is at the end of 5 years.  Accordingly, this outstanding loan balance at the end of 5 years is the present value of the payments still to be made.  Since you still have 25 years left in your contract, it’s reasonable to expect that these (payments) form an annuity of 300 payments [(30 years * 12 months) minus (5 years * 12 months)].  Thus, the outstanding loan balance is:

or $523,614.40
After this, you can now proceed in “working out how long it will take to pay off the mortgage if we increase the monthly repayments by 10% after 5 years of my 30 year loan period”.
Note first that

Thus, with
A = $523,614.40 (loan balance at end of 5 years)
R = $ 3,502.83*1.10 (new monthly payments after 5 years)
j = .064 (nominal interest rate)
m = 12 (interest period, as in monthly - which also happens to be the payment interval)
t = time it takes “to pay off the mortgage if we increase the monthly repayments by 10% after 5 years of my 30 year loan period”

Plugging and chugging, t ≈ 20.21208114 or 20.21 years.  This works out to 242 monthly payments of $3,502.83*1.10 and a smaller payment at the end of the 243rd month (vs. the original remaining 300 monthly payments)

how much extra do we individually have to put in?

This is something that you’re gonna have to work out amongst yourselves.

Assumption B.

lets say the interest compounded quartelrly. The loan was issued 5 June 2002. can you help me go through each step from a) to d)...?

If your interest of 6.4% is compounded quarterly and you wish to pay off the loan monthly, then your problem falls under the general annuity case.  Under this scenario:

a) what amount will I have to repay each month?

The general annuity formula for the present value of an ordinary annuity (i.e. end of interval payment) is given by

where
A = $560,000 (loan amount)
R = monthly payments (to be determined)
j = .064 (nominal interest rate)
m = 4 (interest period, as in quarterly)
t = 30 years (term of loan)
p = 12 (payment interval, as in monthly)

Solving for R gives us: R ≈ 3,490.436822 or $3,490.44
Note: 6.40% compounded quarterly is equivalent to approximately 6.3661668752351% compounded monthly since both have an effective nominal rate of approximately 6.55524495360014%
We show this with the following:

To simplify and to duplicate our discussion of assumption A, we convert this complex annuity problem into its equivalent simple case.  Thus with
A = $560,000 (loan amount)
R = monthly payments (to be determined)
j = .063661668752351 (the equivalent nominal interest rate compounded monthly of 6.40% compounded quarterly)
m = 12 (interest period, as in monthly)
t = 30 years (term of loan)
You then solve for R in the following amortization equation:

Solving for R gives us

b) how much will I have to repay in total on this loan?

There are 360 monthly payment intervals (30 years * 12 months).
Thus, your total payments on this loan would be 360*$3,490.44 or $1,256,558.40.

c) is there any way of working out how long it will take to pay off the mortgage if we increase the monthly repayments by 10% after 5 years of my 30 year loan period

To work out how sooner you can pay off your mortgage if you increase the monthly repayments by 10% after 5 years of your 30 year loan period, you must first work out how much your outstanding loan balance is at the end of 5 years.  Accordingly, this outstanding loan balance at the end of 5 years is the present value of the payments still to be made.  Since you still have 25 years left in your contract, it’s reasonable to expect that these (payments) form an annuity of 300 payments [(30 years * 12 months) minus (5 years * 12 months)].  Thus, the outstanding loan balance is:

or $523,407.17
After this, you can now proceed in “working out how long it will take to pay off the mortgage if we increase the monthly repayments by 10% after 5 years of my 30 year loan period”.
Note first again that

Thus, with
A = $523,407.17 (loan balance at end of 5 years)
R = $3,490.44*1.10 (new monthly payments after 5 years)
j = .063661668752351 (the equivalent nominal interest rate compounded monthly of 6.40% compounded quarterly)
m = 12 (interest period, as in monthly)
t = time it takes “to pay off the mortgage if we increase the monthly repayments by 10% after 5 years of my 30 year loan period”

Plugging and chugging, t ≈ 20.23034792 or 20.23 years.  This also works out to 242 monthly payments of $3,490.44*1.10 and a smaller payment at the end of the 243rd month (vs. the original remaining 300 monthly payments)

how much extra do we individually have to put in?

Again, this is something that you’re gonna have to work out amongst yourselves.

and perhaps even diagrams how I would go about working out this solution

is there any way possible to post a graph here showing my repayments over this period?

If you wish to confirm my solutions with a spreadsheet amortization schedule, either post your email address or a token email address on this thread and I’ll gladly send you two (i.e. assumption A and B).

Last edited by Ms. Bitters (2008-08-26 07:07:54)

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