Need done if possible!

Option2 : Renting

Rent = 550*52*3 = $85800

$$\begin{array}{rll}
Future \;Value\; of \;term\; deposit&=&P(1+i)^n\\\\
&=&112000(1+0.0525/12)^{36}\\\\
&=&\$131,060\\\\
\end{array}$$

Renting Balance after 3 years = 131,060-85800= $45,260

Buying Balance after 3 years = $168,923-$12000 = $156,923

Well, buying appears to be the better option.

I am surprised I will admit, I didn't think the difference wouldbe this great.  

THIS SERVICE IS PROVIDED ON AN "AS IS" AND "AS AVAILABLE" BASIS WITHOUT WARRANTY OF ANY KIND..  (lol)

ethan, what do you mean that about the $1 per week when you rent the house?

You are not supposed to ask us to "do it"

You are supposed to ask us to 'help you'

How much have you done for yourself.  There as many aspects to this problem.

What I mean is that the $1 every week for rent whichwould equivelate to $550 rent per week 

Ive worked out most of the calculations. Pretty much anything in brackets next to the dot points I have worked out but I need help with factoring in the last two dot points of option 1 and I am struggling to work out the last dot point in option 2, I dont mean to ask for you to do it, I meant help, im sorry 

I have a couple of questions of my own in the buying options and I have given you a pointer in the renting option.

--------------------

**You need to work out what the two values-costs are at the end of 3 years.

**This can be done with different degrees on complexity depending on what level you are studying at.

Option 1:Buying a property considering:

• you purchase the property you have chosen ($560,615.26)
• you have your 20% deposit saved ($461,000.00)

Q: Where did $461,000.00 come from??  It is not 20% or 80% of $560615.26

• you make your regular monthly repayments (3032.80) – 6.5%

Q: Is interest charged at 6.5% p.a. ??

• house maintenance expenses are approximately $4 000 a year (haven’t factored)
• property values appreciate by 7.7% per annum. (Haven’t factored)

Option 2: Renting over a period of three years considering:

• You rent a similar property to the one you have chosen. As a general rule, weekly rent payments would be equal to $1 for every $1 000 of the value of the home. (value of home is $550,000 so $550)
• The deposit you have saved (same as in Option 1) will be invested into a term deposit for the three years at 5.25% per annum, compounding monthly (Haven’t done)

How much will the deposit grow to after three years if it is just invested??  This is just a compound interest amount  FV=P(1+r)^n

1st question

Sorry, the 20% is not 461,000 that was for a different house that I had to do!, the 20% is $448,492.208 which then I would need to have rounded up to $449,000 so its per thousand which was for my other questions. 

2nd question 

Yes interest is charged at 6.5% p.a 

Option 2 question 

Oh thank you, I was not sure what Formula would be needed to solve/find the answer to option 2 (dot point 2) 

Option 1 :  Buying

cost = $560,615.26   I'll round off to $560,615

Deposit = 0.20*$560615 = $112,123 = $112,000  (roounded to the nearest thousand - paid in cash)

A= Amount borrowed = $560615 - $112000 = $448,615

Interest on loan = 6.5%pa = 0.065pa :

i = 0.065/12 = 0.0051666666666 per month

R = Regular payment = $3032.80 per month

The time to repay the loan n  must be determined. 

$$\boxed{ \mbox{Present value of an ordinary annuity }\qquad
A=R\times\frac{1-(1+i)^{-n}}{i}}$$

$$\begin{array}{rll}
A&=&R\times\frac{1-(1+i)^{-n}}{i}\\\\
448615&=&3032.80\times\frac{1-1.005416666666666^{-n}}{0.005416666666666}\\\\
\frac{448615\times 0.005416666666666}{3032.80}&=& 1-1.00516666666666^{-n}\\\\
\dfrac{448615\times 0.005416666666666}{3032.80}-1&=& -1.00516666666666^{-n}\\\\
-0.198760908&=& -1.005416666666666^{-n}\\\\
0.198760908&=& 1.005416666666666^{-n}\\\\
log(0.198760908)&=& log(1.005416666666666^{-n})\\\\
log(0.198760908)&=& -n*log(1.005416666666666)\\\\
\frac{log(0.198760908)}{log(1.005416666666666)}&=&-n\\\\
n&=&\frac{-log(0.198760908)}{log(1.005416666666666)} \\\\
n&=&299.08\;months \\\\
Loan\; period&=&25\;years\\
\end{array}$$

So now you need to go backwards to work out how much is owing on the house after 3 years.

22 years of the loan is left = 22*12 = 264 months

$$\begin{array}{rll}
A&=&R\times\frac{1-(1+i)^{-n}}{i}\\\\
A&=&3032.80\times\frac{1-(1.00541666666666)^{-264}}{0.00541666666666}\\\\
A&=&\$425,394\\\\
\end{array}$$

Equity after 3 years without considering appreciation = $560,651 - $425,394 = $135,221

Equity after 3 years considering appreciation = $135,221 * 1.077³ = $168,923

Costs without any adjustments = $12000

Balance after 3 years = $168,923-$12000 = $156,923

Thank you so much!

Ethan has asked some questions via private messaging.

But I will continue answering here.

First I need to try and explain the numbers that my conclusion is based on.

For both renting and buying this person began with $112,000

The rest, rent and repayments was paid for out of future earnings.

The figures below relate to what this person has after 3 years. (This in effect is what the original $112,000 has becomes.)

--------------------------------------

Renting: $112000 + interest on the term deposit - rent = $45,260

The amount has decreased because the cost of the weekly rent is more than the interest that is being earned on the term deposit. So this person has gone backwards he has less than he started with.

Renting Balance after 3 years = 131,060-85800= $45,260

---------------------------------------

Buying: This person will have some equity in his home.  If he sells it he can expact to 'realise' $168,923. The rest will go to the bank to finish the loan. However there have been some expenses along $12000 of expenses along the way so this will have to be deducted. (Just like the rent was deducted)

Buying Balance after 3 years = $168,923-$12000 = $156,923

So after three years if your rent then your saving of $112000 has reduced to $45,260

and if your buy then it has increased to $156,923

Is that a bit clearer now?

I think you sorted out the interest bit yourself?  And yes our answers should  be the same. 

Ethan, I take it you are Australian.  May I ask where/what you are studying?  

I'm just curious, thanks.