Annuities (1 Viewer)

[sally_33]

Can someone please explain question 3 from here to me?

Thanks

Edit: And question 5 as well please!

 

[PC]

Question 3
The table is not well labelled. I suspect that it gives the future value for an investment of $1 at various interest rates over various periods.

Now we're investing $150, so what ever value in the table we use, we just multiply it by $150.

We're investing $150 at 12% per year, which is 1% per month, for 3 months.
The future value of $1 at 1% per month for 3 month is $3.0301.
So the future value of $150 at 1% per month for 3 months is 3.0301 x 150 = 454.515 = $454.52.


Question 5
Whenever you're taking out a loan, always use the PV formula, and the present value is always the amount of the loan.

So for this question we have:
N = $200 000
r = 8.4% p.a. = 0.7% per month = 0.007 (as a decimal)
n = 15 years = 15 x 12 = 180 months
We must assume that interest is calculated at the end of each year.

So:
N = M [ (1 + r)^n – 1 / r(1 + r)^n ]
200000 = M x [ (1 + 0.007)^180 – 1 / 0.007 x (1 + 0.007) ^ 180 ]
200000 = M x [ (1.007)^180 – 1 / 0.007 x (1.007) ^ 180 ]
200000 = M x 102.1568757
M = $1957.77

So monthly repayment is $1957.77.

Hope that helps.

 

[sally_33]

Thanks heaps for that.

I also need help with this one:

Natalie and Andrew take out a loan of $150 000 over 30 years at 8.25% pa interest compounding monthly. Their repayment is $1127 per month. After 5 years of repaying the loan they make a lump sum payment of $40 000.

a) How long will it take to repay the loan?

b) How much is saved by making the lump sum payment?

If anyone could help that would be great. I hate maths but i'd like to at least pass

 

[PC]

Are you using a graphic calculator?

This question is pretty easy for a GC, but very hard without one! (I think - there may be a really quick way of doing this that I'm missing).

Here's what to do with a GC.

(a) First, find the balance owing at the end of the first 5 years.

n = 5 x 12
I = 8.25
PV = -150000
PMT = 1127
FV = ?
P/Y = 12
C/Y = 12

FV = $142 918.56

So there is $142 918.56 owing after 5 years.

Then the lump sum payment of $40 000 is made, so the balance owing then becomes $102 918.56.

Now find the number of payments required to finish paying off the loan.

n = ?
I = 8.25
PV = -102 918.56
PMT = 1127
FV = 0
P/Y = 12
C/Y = 12

n = 144.2618111

So it would take an additional 145 months to pay off the loan.

So altogether it would take 60 + 145 or 205 months (17 years and 1 month) to pay off the loan.

Note: The final payment won't be exactly $1127, but probably something like $295.79 just to finish off the loan. This means that the answer to (b) will only be a very close estimate.

(b) Assuming the final payment was $1127:

The total repaid by Natalie and Andrew was 205 payments of $1127 plus the lump sum payment of $40000.
Total repaid = (205 x 1127) + 40000
= $271035

If the lump sum wasn't made, then the loan takes 30 years (360 months) to repay.
Total to repay = 360 x 1127
= $405720

So amount saved = 405720 – 271035
= $134685

And that's not bad for a payment of $40000!


Is there a way of doing this question using the formulae given in the general course rather than a GC? This is a good question for the 2u and 3u guys to do with GPs! Have you challenged your friends with this?

 

[sally_33]

Wow thanks for all that but im not using a graphics calculator.

The answer for (a) says 17 years 1 month anyway though???

This question is just from my normal textbook so it shouldnt be too hard?? its from a revision test in the textbook.

Is there a way of doing this question using the formulae given in the general course rather than a GC?

This is from the annuities topic so the only formulas given in that topic are Future value and present value??


Do you think i should ring up the advice line and ask or does anyone know how to do it??

 

[PC]

Your book is right.

My answer of 144.261... should mean 145, not 143, so that means 17 years 1 month instead of 16 years 11 months.

I've got to work on my rounding!

You can try the advice line if you're really keen on knowing how to do this question, but I wouldn't worry about it too much. I reckon it's a bit too hard for the course and I doubt you'll see a question this hard on Monday arvo ... but you never know.

Maybe monitor this thread for a while and see if someone can answer it for you.

Does your book have a worked solution? Or just the answer? I'd be keen to see how they get their answer.

 

[sally_33]

yeah the book doesnt have a worked solution, just straight answers

thanks for your help anyway though

i guess ill just not bother if no-one else has a way of answering it without a graphics calculator

 

[shimmerme]

ok.. i have a question from the questions linked at the beginning of this thread- question one?? ..me and it are at war, and i am not winning, lol

Jody deposits $150 per month in an account earning 6.8% interest p.a.

If the interest is compounded monthly, what is the amount in her account after 10 years.

..any ideas? please

 

[Muzzaw]

ok.. i have a question from the questions linked at the beginning of this thread- question one?? ..me and it are at war, and i am not winning, lol

Jody deposits $150 per month in an account earning 6.8% interest p.a.

If the interest is compounded monthly, what is the amount in her account after 10 years.

..any ideas? please

Yeah, use the future value formula and sub in these values.

M = 150
r = 0.068/12
= .0056....
n = 10 x 12
= 120
A = ?

 

[Muzzaw]

$25,678.92 ?

 

[danieljarvis]

yep .. 1234567890

 

[H.S.What?]

hey i got this question in a maths book:

Samantha borrows $20,000 from her grandmother and repays it in equal monthly instalments over 6 years. The interest rate is 1% per month.

a) what is the amount of each instalment?

b) how much does Samantha have to repay?

c)Her grandmother takes the interest that Samantha has paid and invests it for a further 4 years at 9% p.a. interest compounded monthly before returning it to Samantha as a present. How much will Samantha receive?

for parts a) and b) i assumed you are supposed to use I = Prn formula however i got $14,400 total interest she has to pay when the textbook says $8152 interest. I used the present value formula for annuities to see what i got and i got the answer in the book (?)

N = M { (1+0.01)^72 - 1) / 0.01(1+0.01)^72) }

was i wrong in using the simple interest formula?

 

[H.S.What?]

disregard my last post, i called the advice line and the guy said that if the question is in period repayments u use the present value or future value formulas, if its in lump sum amounts its the simple/compound interest formula

 

[anita_wax]

Question 3
The table is not well labelled. I suspect that it gives the future value for an investment of $1 at various interest rates over various periods.

Now we're investing $150, so what ever value in the table we use, we just multiply it by $150.

We're investing $150 at 12% per year, which is 1% per month, for 3 months.
The future value of $1 at 1% per month for 3 month is $3.0301.
So the future value of $150 at 1% per month for 3 months is 3.0301 x 150 = 454.515 = $454.52.


Question 5
Whenever you're taking out a loan, always use the PV formula, and the present value is always the amount of the loan.

So for this question we have:
N = $200 000
r = 8.4% p.a. = 0.7% per month = 0.007 (as a decimal)
n = 15 years = 15 x 12 = 180 months
We must assume that interest is calculated at the end of each year.

So:
N = M [ (1 + r)^n – 1 / r(1 + r)^n ]
200000 = M x [ (1 + 0.007)^180 – 1 / 0.007 x (1 + 0.007) ^ 180 ]
200000 = M x [ (1.007)^180 – 1 / 0.007 x (1.007) ^ 180 ]
200000 = M x 102.1568757
M = $1957.77

So monthly repayment is $1957.77.

Hope that helps.

as said in other post i dont get how you got from 102$ to 1957$
what is m?

 

[H.S.What?]

M is the amount of the monthly repayment/instalments. I dont know where you got the $102 figure from

 

[sally_33]

as said in other post i dont get how you got from 102$ to 1957$
what is m?

he just solved the equation

200 000 = M x 102.1568757


so to get M on its own divide 200 000 by 102.1568757

therefore M = $1957.77

 

[anita_wax]

he just solved the equation

200 000 = M x 102.1568757


so to get M on its own divide 200 000 by 102.1568757

therefore M = $1957.77

ah thats what i was looking for. ty vm now i understand

 

[Muzzaw]

disregard my last post, i called the advice line and the guy said that if the question is in period repayments u use the present value or future value formulas, if its in lump sum amounts its the simple/compound interest formula

What did he mean by period payments and lump sum amounts?

Example?

 

[sally_33]

i think it just means

period payments e.g. $500 at the end of each month

lump sum e.g. $10000 as a one payment

 

[spartan 117]

M is the amount of the monthly repayment/instalments. I dont know where you got the $102 figure from

your kidding me right, u must be blind, look harder....