Maths of finance qs... (1 Viewer)

ToO LaZy ^* · Jun 12, 2005

yo fellers.

ive got me a few questions from the yellow finance book that i dont know how to do...so if any of you geniuses can help that would be super.

2.15
You may pay HECS fees in a lump sum of $1500 now or pay three equal instalments of $800 at the beginning of years 5,6 and 7. (Assume now is the beginning of year 1 and r=0.1). Which method of payment is better in monetary terms?
answer: PV = $1494.73 better to pay later.

2.16
[solved]

if you can get these answers, could you post up your workings...or explain how you did it plz?

peace out.

sarevok · Jun 12, 2005

Pv = 800(1+0.1)^-4 + 800(1+0.1)^-5 + 800(1+.1)^-6 = 1494.73

ToO LaZy ^* · Jun 12, 2005

argh. can't believe i missed that..'beginning'..pftt.

thx man..

many more qs to come

ToO LaZy ^* · Jun 12, 2005

more questions...

2.17
Suppose you have a debt of $8000. Your first payment is $3000, due at the end of year 3. You also must make 2 additional and equal payments of $X, due at the end of Years 1 and 4. Find X, given r = 0.1
answer: $3609.10

2.19
david borrows $4000 at 10%p.a. compounded quarterly. he promises to pay $1000 at the end of the first year, $2000 at the end of the second year and the balance at the end of the third year. what will the final payment be?
answer: $1953.53

2.23
in discharging a debt of $10000 with interest at 4% compounded semi-annually, Belinda agrees to make two equal payments of X, the first due in 6 months and the second due in 5 years, with a final payment of $2500 one year later. Find X.
answer: $4458.59

Cheers

sarevok · Jun 12, 2005

2.17

8000 = 3000(1+0.1)^-3 + X(1+0.1)^-1 + X(1+0.1)^-4

8000 - 3000(1+0.1)^-3 = X(1+0.1)^-1 + X(1+0.1)^-4

X = (8000 - 3000(1+0.1)^-3)/1.592104364

X = 3609.10

cant find my working for the others atm

ToO LaZy ^* · Jun 12, 2005

cool.
oh, and a general question..
just say for this question..

2.26
suppose you wish to borrow $20K to buy a car. the finance company offers interest of 18%p.a. compounded monthly for 4 years. what is the size of the monthly repayment?...

how do you work out if we use present value or future value??

kow_dude · Jun 13, 2005

ToO LaZy ^* said:
2.19
david borrows $4000 at 10%p.a. compounded quarterly. he promises to pay $1000 at the end of the first year, $2000 at the end of the second year and the balance at the end of the third year. what will the final payment be?
answer: $1953.53

1st year: 4000 (1 + 0.1/4 )^4
= 4415.25156
= 4415.25156 - 1000
= 3415.25156

2nd year: 3415.25156 (1 + 0.1/4)^4
= 3769.7987
= 3769.7987 - 2000
= 1769.7987

3rd year: 1769.7987 (1+ 0.1/4)^4
= 1953.523

kow_dude · Jun 13, 2005

ToO LaZy ^* said:
more questions...

2.23
in discharging a debt of $10000 with interest at 4% compounded semi-annually, Belinda agrees to make two equal payments of X, the first due in 6 months and the second due in 5 years, with a final payment of $2500 one year later. Find X.
answer: $4458.59

I'm not sure about my solution because i got answer: 4460.426

1st payment: P = X( 1 + 0.04/2 )^(-0.5 x 2)
= 0.980392156

2nd payment: P = X( 1 + 0.04/2 )^(-5 x 2)
= 0.820348299

PV of final payment: P = 2500 ( 1 + 0.04/2 )^(-6x2)
= 1971.232939

10000 = 0.980392156X + 0.820348299X + 1971.232939
X = 4460.426

Eagles · Jun 13, 2005

kow_dude said:
I'm not sure about my solution because i got answer: 4460.426

1st payment: P = X( 1 + 0.04/2 )^(-0.5 x 2)
= 0.980392156

2nd payment: P = X( 1 + 0.04/2 )^(-5 x 2)
= 0.820348299

PV of final payment: P = 2500 ( 1 + 0.04/2 )^(-6x2)
= 1971.232939

10000 = 0.980392156X + 0.820348299X + 1971.232939
X = 4460.426

I'd say thats just a rounding error..

I converted my payments into months

10k = 2500(1.02)^-12 + X(1.02)^-10 + X(1.02)^-1

which gives X = 4458.592037..

Eagles · Jun 13, 2005

ToO LaZy ^* said:
how do you work out if we use present value or future value??

The question will tell you.. If you want to have X amount in Y years, then its a FV.

Paying off loans are PV.

btw, is the answer $587.4999922?

kow_dude · Jun 14, 2005

Could someone tell me how to use the Annuity tables. For exampe, how do i work out 2.24 (a) using the tables rather than the formulas?

ToO LaZy ^* · Jun 14, 2005

the formula for PV is Ra_n|r
= 200a_20|0.02

so we go the the tables for PV and look for the rate: 2% on the horizontal values and the number of periods (vertical) and it turns out to be 16.3514333

= 200 X 16.3514333
= 3270.28666

ToO LaZy ^* · Jun 14, 2005

Eagles said:
I'd say thats just a rounding error..

I converted my payments into months

10k = 2500(1.02)^-12 + X(1.02)^-10 + X(1.02)^-1

which gives X = 4458.592037..

i don't understand the "X(1.02)^-10 + X(1.02)^-1" bit...why are you using the values -10 and -1?

kow_dude · Jun 14, 2005

ToO LaZy ^* said:
i don't understand the "X(1.02)^-10 + X(1.02)^-1" bit...why are you using the values -10 and -1?

The value -1 was used because the first payment was due in 6 months and compunded semi-annually. Therefore, 0.5 x 2 = 1

The value -10 was used because the second payment was due in 5 years and compunded semi-annually. Therefore, 5 x 2 = 10

(They are negative 10 and 1 because it's -nt)

ToO LaZy ^* · Jun 14, 2005

*excellent*..

ok, this is from the revision qs..

Q48.
Suppose that you are prepared to deposit $100 per month into an account so that in 3 years time when you graduate, you will be able to go on an overseas holiday which costs $5000. Assume that the interest rate is 12% pa compounded monthly. How much extra money must you have saved in order to be able to afford this holiday?

ANSWER: $649.24

Eagles · Jun 15, 2005

ToO LaZy ^* said:
*excellent*..

ok, this is from the revision qs..

Q48.
Suppose that you are prepared to deposit $100 per month into an account so that in 3 years time when you graduate, you will be able to go on an overseas holiday which costs $5000. Assume that the interest rate is 12% pa compounded monthly. How much extra money must you have saved in order to be able to afford this holiday?

ANSWER: $649.24

5000 - (100(1.01^35) + 100(1.01^34) + ... + 100)

= 5000 - [100 * (1.01^36 - 1) / 0.01]

= 692.3121641...

did he deposit at the beginning of each month or did he wait till the end of the 1st month to deposit his 100?

ok, according to your answer, it's an annunity due problem.

5000 - [100 * (1.01^36 - 1)(1.01) / 0.01 ]

= 649.2352857

yvonne_710 · Jun 15, 2005

Eagles said:
5000 - (100(1.01^35) + 100(1.01^34) + ... + 100)

= 5000 - [100 * (1.01^36 - 1) / 0.01]

= 692.3121641...

did he deposit at the beginning of each month or did he wait till the end of the 1st month to deposit his 100?

ok, according to your answer, it's an annunity due problem.

5000 - [100 * (1.01^36 - 1)(1.01) / 0.01 ]

= 649.2352857

Tig said its time difference here. thats why we need to time 1.01, one more month extra.. Tig gave us is 5000 - [100*(36^0.01)]*1.01
is it the same thing?

Eagles · Jun 15, 2005

yvonne_710 said:
Tig said its time difference here. thats why we need to time 1.01, one more month extra.. Tig gave us is 5000 - [100*(36^0.01)]*1.01
is it the same thing?

I'm not sure what you guys are taught, but we call it an annunity due problem over at unsw, which just means payment made at the beginning of the month.

basically, here's what I did:

yvonne_710 · Jun 15, 2005

Eagles said:
I'm not sure what you guys are taught, but we call it an annunity due problem over at unsw, which just means payment made at the beginning of the month.

basically, here's what I did:

my lecturer said in the qs, we need to pay one more extra, thats why times 1.01, i only know this.....errrrrrr

sarevok · Jun 15, 2005

I'm not sure where the question indicates that it is an annuity due?

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