Interest and monthly repayment help!! Urgent plz...

**tom_asian** · August 10th 2007, 09:23 PM

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

**CaptainBlack** · August 10th 2007, 10:17 PM

Originally Posted by tom_asian

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:

$ S=1.04^4 \times 60000 \approx \$ 70191.51 $

So the maximum monthly payments allowed will be:

$ M=S/12 \times 0.25 \approx \$ 1462.32 $

RonL

**CaptainBlack** · August 10th 2007, 11:23 PM

Originally Posted by tom_asian

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:

$ (1+MR/100)^{12} = 1.0656 $

so:

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

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

$ D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301} $ ,

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 $\$1462.32$ :

$ L\times 1.005301^{180} - 1462.32\frac{1-1.005301^{179}}{1-1.005301}=0 $

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

**CaptainBlack** · August 11th 2007, 08:17 AM

Originally Posted by tom_asian

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

**jungohyj** · August 12th 2007, 07:16 AM

Originally Posted by CaptainBlack

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?

**CaptainBlack** · August 12th 2007, 10:41 AM

Originally Posted by jungohyj

Where does 0.035 come from?

It should be OK now.

RonL

**tom_asian** · August 12th 2007, 10:43 PM

Originally Posted by CaptainBlack

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:

$ S=1.04^4 \times 60000 \approx \$ 70191.51 $

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

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 >>
$ S=1.04^3 \times 60000 \approx \$ 67491.84 $

**CaptainBlack** · August 12th 2007, 10:50 PM

Originally Posted by tom_asian

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 >>
$ S=1.04^3 \times 60000 \approx \$ 67491.84 $

OK, next time I will read it more carefully.

RonL

**tom_asian** · August 12th 2007, 11:22 PM

Originally Posted by CaptainBlack

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:

$ (1+MR/100)^{12} = 1.0656 $

so:

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

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

$ D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301} $ ,

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 $\$1462.32$ :

$ L\times 1.005301^{180} - 1462.32\frac{1-1.005301^{179}}{1-1.005301}=0 $

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?
$ D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301} $ ,
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~~~

**CaptainBlack** · August 12th 2007, 11:41 PM

Originally Posted by tom_asian

Hello. Could I also please check what formula does this come from?
$ D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301} $ ,
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

**tom_asian** · August 12th 2007, 11:59 PM

Originally Posted by CaptainBlack

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

$ D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301} $ ,

Its just that i need to know the name of this formula before i can use it. Thanks ^^

**CaptainBlack** · August 13th 2007, 02:21 AM

Originally Posted by tom_asian

Sorry but is there a specific name for this formula?

e.g annuity formula or something like that

$ D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301} $ ,

Its just that i need to know the name of this formula before i can use it. Thanks ^^

No idea i'm afraid

RonL

**TKHunny** · August 13th 2007, 03:16 PM

Originally Posted by tom_asian

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'.

**CaptainBlack** · August 13th 2007, 07:46 PM

Originally Posted by tom_asian

Sorry but is there a specific name for this formula?

e.g annuity formula or something like that

$ D(n)=L\times 1.005301^n - p\frac{1-1.005301^{n-1}}{1-1.005301} $ ,

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

**tom_asian** · August 14th 2007, 12:52 AM

Originally Posted by CaptainBlack

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

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