Annoying loan question!! (1 Viewer)

[Dr_Doom]

Hi, I've been trying to answer this for like 30 mins. It's frikin annoying lol. Well here it is. If anyone knows how to solve it. Please write it here.

It's on page 104 of the new centry maths book. Question 9. (c)

Well here it is:

9. Edita has a gross income of $52000 p.a. and wants to purchase a studio apartment. The bank will allow her to repay up to 20% of her gross income per annum. The current loan rate is 6.84% p.a. and fees and charges amount to $4000. She wants to borrow the maximum possible and make monthly repayments.

(c) What amount will the bank lend Edita over 10 years?

At first, I thought the answer was $104,000. Because that's 20% of her income [times] 10 years.

The answer is $75,176

I dunno how to get that. I'll prolly figure it out later..... But if I don't can someone attempt it????

Thanks!

 

[Dr_Doom]

It's simple interest so maybe...

I=PRN
104000 = P x 0.0648 x 10
P = 104000 / 0.648
P = 160493.8272 - 4000
P = $156,493.83

NOPE!

 

[Dr_Doom]

Ok I think it's impossible.

I tried it with the answer and look..

I = 75176 x 0.0648 x 10
I = $48,714.05

Screw this!

 

[SoulSearcher]

Lol, I'm using the 2 unit formula for loan repayments here, but it still gets you the answer you are looking for.

now the formula is A_n = PRⁿ - M(Rⁿ -1)/R-1
where
A_n is the amount left to be repaid after n repayments
P is the initial loan given
M is the amount of the repayment
R is equal to 1 + the interest rate given in decimals
n is the amount of repayments
Now we have to find P, the original amount the bank has loaned her.
so, for your question, since she wants to pay monthly repayments, the monthly repayment is $866.67, n is 12*10 = 120, and thus the rate has to be calculated in months, which is 0.0684/12 = 0.0057, therefore total interest rate is 1.0057
A₁₂₀ = P(1.0057)¹²⁰ - 866.67 * (1.0057¹²⁰ - 1)/(1.0057-1)
but since the loan is to be repayed at the end of 10 years, A₁₂₀ = 0
0 = P(1.0057)¹²⁰ - 866.67 * (1.0057¹²⁰ - 1)/(1.0057-1)
P(1.0057)¹²⁰ = 866.67 * (1.0057¹²⁰ - 1)/(1.0057-1)
P = { 866.67 * (1.0057¹²⁰ - 1)/(1.0057-1) } / { (1.0057)¹²⁰ }
P = $75, 176, which is the largest amount the bank can lend Edita over the 10 years, which is your answer.
EDIT (my rounding off's screwed )

 

[Dr_Doom]

All I can say is WOW! and you're $1 off

Who would have thought a 2U question would be in a general book. I'm screwed if I get that in my HSC.....

Thanks though for telling me the answer,
Cheers

 

[PC]

This question is in the flat rate loan section of the text book, so I'd say that you use simple interest.

Here's my working:

(a) (i)
Maximum annual repayment
= 20% of gross income
= 0.20 x 52000
= $10400

(a) (ii)
Maximum monthly repayment
= 10400 ÷ 12
= $866.67

(b)
Amount borrowed = $150000
Fees & charges = $4000
Principal = 150000 + 4000 = $154000

Now I = Prn
Interest = 154000 x 0.0684 x 10
= $105336
Amount to repay = Principal + Interest
= 154000 + 105336
= $259336
Annual repayment = 259336 ÷ 10
= $25933.60

Since this is more than the maximum annual repayment that Edita can make, the bank will not loan her the money.

(c) Over 10 years, Edita can pay $10400 per year.
Total she can repay = 10400 x 10
= $104 000

So P + I = 104000
I = 104000 – P

Now I = Prn
104000 – P = P x 0.0684 x 10
104000 – P = 0.684P
104000 = 0.684P + P
104000 = 1.684P
P = 104000 ÷ 1.684
P = $61757.72

Don't forget that this includes $4000 in fees & charges, so the maximum amount that Edita can borrow is $57 757.72

Obviously not in line with the given answer.

Otherwise you'd have to resort to the present value formula.
We know maximum monthly payment is $866.67
We know that the interest rate is 6.84% p.a. or 0.57% per month.
We know that the loan is to be repaid over 10 years or 120 months.

So N=M[(1+r)^n – 1 / r(1+r)^n]
= 866.67 x [(1+0.0057)^120–1 / 0.0057(1+0.0057)^120]
= 866.67 x [1.0057^120–1 / 0.0057(1.0057)^120]
= 866.67 x [0.9779441084/0.01127428142]
= 75175.95
Don't forget to take off the $4000 in fees and charges, so the amount borrowed is $71175.95

That's a bit better.

I wonder if the book was intending that the question be answered by setting up a reducible balance table?

 

[Dr_Doom]

It can't be a balance table because you wouldn't know the starting price or principal.
The first method you did should have worked. It's weird...