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Math Help - Interest and monthly repayment help!! Urgent plz...

  1. #1
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    Exclamation Interest and monthly repayment help!! Urgent plz...

    Hey. Could somebody please help me. Thank you ~~


    Info given:

    Bec Bank
    Minimum deposit - 10% of sale price
    Application fee - $600
    Term of Loan - 15,20 or 25 years
    Interest rate (% p.a. fixed) - 6.25% p.a compounded daily
    Maximum Monthly Repayment Criteria - 25% of gross monthly income

    Kaitlyn credit union
    Minimum deposit - 5% of sale price
    Application fee - Nil
    Term of Loan - 15,20 or 25 years
    Interest rate (% p.a. fixed) - 6.35% p.a compounded daily
    Maximum Monthly Repayment Criteria - 25% of gross monthly income

    salary = $60000

    __________________________________________________ ______

    a) Assuming that your salary increases by 4% pa calculate the salary at the start of the fourth year and the maximum monthly repayment allowed by the bank and credit union at this time.

    b) Using the amount that you calculated in a) calculate the loan amounts that you would be able to borrow For both the bank and the credit union you must calculate the amount that could be borrowed over 15, 20 or 25 year. Full working must be included for one of these calculations and the other 5 may be done on your calculator The data you enter for these calculations must be included in your working.

    c) Calculate the maximum loan amount that you would be allowed to borrow at that time. Show working to justify that your savings satisfy the criterion for the deposit. Note. When considering the bank loan the application fee comes out of your savings before any other calculations are considered.


    You help would be greatly appreciated... Thanks alot
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  2. #2
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    Quote Originally Posted by tom_asian View Post
    Hey. Could somebody please help me. Thank you ~~


    Info given:

    Bec Bank
    Minimum deposit - 10% of sale price
    Application fee - $600
    Term of Loan - 15,20 or 25 years
    Interest rate (% p.a. fixed) - 6.25% p.a compounded daily
    Maximum Monthly Repayment Criteria - 25% of gross monthly income

    Kaitlyn credit union
    Minimum deposit - 5% of sale price
    Application fee - Nil
    Term of Loan - 15,20 or 25 years
    Interest rate (% p.a. fixed) - 6.35% p.a compounded daily
    Maximum Monthly Repayment Criteria - 25% of gross monthly income

    salary = $60000

    __________________________________________________ ______

    a) Assuming that your salary increases by 4% pa calculate the salary at the start of the fourth year and the maximum monthly repayment allowed by the bank and credit union at this time.
    Your salary grows by a factor of 1.04 each year (that is 1+r/100, where r is
    the percentage annual growth. So after four years your salary will be:

    <br />
S=1.04^4 \times 60000 \approx \$ 70191.51<br />

    So the maximum monthly payments allowed will be:

    <br />
M=S/12 \times 0.25 \approx \$ 1462.32<br />

    RonL
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  3. #3
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    Quote Originally Posted by tom_asian View Post
    Hey. Could somebody please help me. Thank you ~~


    Info given:

    Bec Bank
    Minimum deposit - 10% of sale price
    Application fee - $600
    Term of Loan - 15,20 or 25 years
    Interest rate (% p.a. fixed) - 6.25% p.a compounded daily
    Maximum Monthly Repayment Criteria - 25% of gross monthly income

    Kaitlyn credit union
    Minimum deposit - 5% of sale price
    Application fee - Nil
    Term of Loan - 15,20 or 25 years
    Interest rate (% p.a. fixed) - 6.35% p.a compounded daily
    Maximum Monthly Repayment Criteria - 25% of gross monthly income

    salary = $60000

    __________________________________________________ ______



    b) Using the amount that you calculated in a) calculate the loan amounts that you would be able to borrow For both the bank and the credit union you must calculate the amount that could be borrowed over 15, 20 or 25 year. Full working must be included for one of these calculations and the other 5 may be done on your calculator The data you enter for these calculations must be included in your working.
    Now there is a difficulty here, a financial institution that compounds interest
    daily is going to allow for the differeing length of each month and leap years.

    I don't intend to do that, I will treat each year as comprising 365 days, and there being 12 equal months in a year.

    I will do the 15 year loan for Kaitlyn credit union.

    Interest rate 6.35 \% compounded daily, so the amount due after one year is (1+0.0635/365)^{365} \approx 1.0656 on the dollar so the annual equivalent rate is \approx 6.56 \%.

    The equivalent monthly rate as a percentage MR is such that:

    <br />
(1+MR/100)^{12} = 1.0656<br />

    so:

    MR=\left[ 1.0656^{1/12}-1 \right]-1 \approx 0.5301 \%

    So the outstanding debt after n repayments of \$p is:

    <br />
D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301}<br />
,

    where L is the loan amount. For a 15 year loan, the repayment period is 180 periods of a nominal month, and the outstanding debt is zero, so if the monthly repayment is \$1462.32:

    <br />
L\times 1.005301^{180} - 1462.32\frac{1-1.005301^{179}}{1-1.005301}=0<br />

    Solving this gives L = \$ 167894.34, and to find the price of the property you need to allow for the deposit which will inflate this to:  \$ 167894.34 \times 1.05

    (Note I would not normally count the deposit as part of the loan myself but then UK/US conventions on this may vary)

    RonL
    Last edited by CaptainBlack; August 12th 2007 at 10:41 AM. Reason: correct arithmetic error
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  4. #4
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    Quote Originally Posted by tom_asian View Post
    Hey. Could somebody please help me. Thank you ~~


    Info given:

    Bec Bank
    Minimum deposit - 10% of sale price
    Application fee - $600
    Term of Loan - 15,20 or 25 years
    Interest rate (% p.a. fixed) - 6.25% p.a compounded daily
    Maximum Monthly Repayment Criteria - 25% of gross monthly income

    Kaitlyn credit union
    Minimum deposit - 5% of sale price
    Application fee - Nil
    Term of Loan - 15,20 or 25 years
    Interest rate (% p.a. fixed) - 6.35% p.a compounded daily
    Maximum Monthly Repayment Criteria - 25% of gross monthly income

    salary = $60000


    c) Calculate the maximum loan amount that you would be allowed to borrow at that time. Show working to justify that your savings satisfy the criterion for the deposit. Note. When considering the bank loan the application fee comes out of your savings before any other calculations are considered.
    You have not told us what our savings are.

    Other than that, when you have done part b) you have a list of loans that
    you can get given your salary.

    What you have to do with this question is check which loans you can take
    with our savings, and if our savings do not suffice what the maximum loan we
    can take with the savings we do have, for each of the schemes investigated
    in part b).

    RonL
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    Interest rate compounded daily, so the amount due after one year is on the dollar so the annual equivalent rate is
    Where does 0.035 come from?
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  6. #6
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    Quote Originally Posted by jungohyj View Post
    Where does 0.035 come from?
    It should be OK now.

    RonL
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  7. #7
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    Quote Originally Posted by CaptainBlack View Post
    Your salary grows by a factor of 1.04 each year (that is 1+r/100, where r is
    the percentage annual growth. So after four years your salary will be:

    <br />
S=1.04^4 \times 60000 \approx \$ 70191.51<br />

    So the maximum monthly payments allowed will be:
    <br />
M=S/12 \times 0.25 \approx \$ 1462.32<br />

    RonL

    I have a query with the n value which you put into the formula. The question said at the start of the fourth year. Wouldnt the n value be 3, not 4 ?

    like this >>
    <br />
S=1.04^3 \times 60000 \approx \$ 67491.84<br />
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  8. #8
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    Quote Originally Posted by tom_asian View Post
    I have a query with the n value which you put into the formula. The question said at the start of the fourth year. Wouldnt the n value be 3, not 4 ?

    like this >>
    <br />
S=1.04^3 \times 60000 \approx \$ 67491.84<br />
    OK, next time I will read it more carefully.

    RonL
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  9. #9
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    Quote Originally Posted by CaptainBlack View Post
    Now there is a difficulty here, a financial institution that compounds interest
    daily is going to allow for the differeing length of each month and leap years.

    I don't intend to do that, I will treat each year as comprising 365 days, and there being 12 equal months in a year.

    I will do the 15 year loan for Kaitlyn credit union.

    Interest rate 6.35 \% compounded daily, so the amount due after one year is (1+0.0635/365)^{365} \approx 1.0656 on the dollar so the annual equivalent rate is \approx 6.56 \%.

    The equivalent monthly rate as a percentage MR is such that:

    <br />
(1+MR/100)^{12} = 1.0656<br />

    so:

    MR=\left[ 1.0656^{1/12}-1 \right]-1 \approx 0.5301 \%

    So the outstanding debt after n repayments of \$p is:

    <br />
D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301}<br />
,

    where L is the loan amount. For a 15 year loan, the repayment period is 180 periods of a nominal month, and the outstanding debt is zero, so if the monthly repayment is \$1462.32:

    <br />
L\times 1.005301^{180} - 1462.32\frac{1-1.005301^{179}}{1-1.005301}=0<br />

    Solving this gives L = \$ 167894.34, and to find the price of the property you need to allow for the deposit which will inflate this to:  \$ 167894.34 \times 1.05

    (Note I would not normally count the deposit as part of the loan myself but then UK/US conventions on this may vary)

    RonL
    Hello. Could I also please check what formula does this come from?
    <br />
D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301}<br />
,
    Sorry, I havent seen this formula before so just need to know.

    My friend worked it out using the present value of annuity formula x monthly repayment

    [1 - (1 + 0.005301)^-180 ] / 0.005301 x 1406.08 = 162835.88.

    Would this also be the same or your method is more accurate?

    Thanks Ron~~~
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    Quote Originally Posted by tom_asian View Post
    Hello. Could I also please check what formula does this come from?
    <br />
D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301}<br />
,
    Sorry, I havent seen this formula before so just need to know.

    My friend worked it out using the present value of annuity formula x monthly repayment

    [1 - (1 + 0.005301)^-180 ] / 0.005301 x 1406.08 = 162835.88.

    Would this also be the same or your method is more accurate?

    Thanks Ron~~~
    Remaining debt after one repayment period:

    D(1)=L*(1+r)-p

    after two periods:

    D(2)=D(1)*(1+r) - p = L*(1+r)^2 - p[1+(1+r)]

    after three periods:

    D(3) = D(2)*(1+r) - p = L*(1+r)^3 - p[1+(1+r)+(1+r)^2]

    After n periods:

    D(n) = L*(1+r)^n - p[1+(1+r)+(1+r)^2+ .. + (1+r)^{n-1}]

    Then the given formula should follow by summing the series in the [] brackets
    (its a geometric series and so you should be able to right its sum down immediately)

    RonL
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    Lightbulb name of formula?

    Quote Originally Posted by CaptainBlack View Post
    Remaining debt after one repayment period:

    D(1)=L*(1+r)-p

    after two periods:

    D(2)=D(1)*(1+r) - p = L*(1+r)^2 - p[1+(1+r)]

    after three periods:

    D(3) = D(2)*(1+r) - p = L*(1+r)^3 - p[1+(1+r)+(1+r)^2]

    After n periods:

    D(n) = L*(1+r)^n - p[1+(1+r)+(1+r)^2+ .. + (1+r)^{n-1}]

    Then the given formula should follow by summing the series in the [] brackets
    (its a geometric series and so you should be able to right its sum down immediately)

    RonL


    Sorry but is there a specific name for this formula?

    e.g annuity formula or something like that

    <br />
D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301}<br />
,


    Its just that i need to know the name of this formula before i can use it. Thanks ^^
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  12. #12
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    Quote Originally Posted by tom_asian View Post
    Sorry but is there a specific name for this formula?

    e.g annuity formula or something like that

    <br />
D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301}<br />
,


    Its just that i need to know the name of this formula before i can use it. Thanks ^^
    No idea i'm afraid

    RonL
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    Quote Originally Posted by tom_asian View Post
    Its just that i need to know the name of this formula before i can use it. Thanks ^^
    Steve?

    Why does a formula need a name? It is not a reasonable requirement. You should get over that need.

    My views. I welcome others'.
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  14. #14
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    Quote Originally Posted by tom_asian View Post
    Sorry but is there a specific name for this formula?

    e.g annuity formula or something like that

    <br />
D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301}<br />
,


    Its just that i need to know the name of this formula before i can use it. Thanks ^^
    You could just think or it as the future value of the loan after n years minus the future value of the repayments made in n years.

    RonL
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  15. #15
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    Lightbulb

    Quote Originally Posted by CaptainBlack View Post
    You have not told us what our savings are.

    Other than that, when you have done part b) you have a list of loans that
    you can get given your salary.

    What you have to do with this question is check which loans you can take
    with our savings, and if our savings do not suffice what the maximum loan we
    can take with the savings we do have, for each of the schemes investigated
    in part b).

    RonL
    Hello.~~

    I still cant work out how to do with qus c.

    My savings is $29, 013.

    I have taken the application fee from my savings which my new savings is:

    Bec's Bank Kaitlyn
    $29 013 - 600 = $28413 $29013 - 0 = $29013

    The list of loan amounts are:

    Bec bank Kaitlyn
    L 15 yrs - $162 444 .48
    L 20 yrs - $190 744 .89
    L 25 yrs - $211 471 .08

    Kaitlyn
    L 15 yrs - $ 161 437 .22
    L 20 yrs - $ 189 275 .87
    L 25 yrs - $ 209 547 .15


    Could you please help me get around this problem as i dont know what to do next. Could you please provide an example with one set of working out so i can analyse it and see what is going on so i can work out the others,

    Thanks so much for your help
    Last edited by tom_asian; August 14th 2007 at 01:09 AM.
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