Sequences and Series (1 Viewer)

[-pari-]

having trouble when the question doesn't give you "a" (ie the first number of the series) and you're left to work with percentages instead:

a) the price of shares in a particular company is falling by an average of 2% each day.
How many days will it take for the share to halve in value?

Tn = ar^ (n-1)

Tn = 50 (right?)

I let a = 100 (100%?) and r = 0.98
50 = 100 x 0.98^(n-1)
0.5 = 0.98^(n-1)

Through trial and error I made the bases the same (is there any other quicker way? – apart from taking logs) 0.5 approx = 0.98^(13.5)
.’. 13.5 = n – 1
n = 14.5

but the answer is 13.5 …where did I go wrong?

(b) after how many days will the shares be worth 25% of their value? My answer for this one was even more off track:

I got something on the lines of
0.98 ^(64 or something ) = ¼
.’. 64 = n-1
etc

but the answer is 31.4

 

[watatank]

having trouble when the question doesn't give you "a" (ie the first number of the series) and you're left to work with percentages instead:

a) the price of shares in a particular company is falling by an average of 2% each day.
How many days will it take for the share to halve in value?

I'd use the compound interest (or in this case depreciation) formula for that question.

A = P(1-R)^n is the depreciation formula

if P is the share price P/2 will be the halved price after a period of time

P/2 = P(1-0.02)^n

(P's cancel each other out)

0.5 = (0.98)^n

log 0.5 = log (0.98^n)

log 0.5 = n log (0.98)

n = log 0.5/ log (0.98)

Hmm that equals 34.3 days...

 

[SoulSearcher]

I suggest actually using logs with these questions, it is a lot quicker, makes the work a lot easier, and leads to less mistakes than trial and error.

For the first one, I'm getting 34.3 days as well.
The second one, n = ln 0.25 / ln 0.98 = 68.6 days, well it should be anyway. Must be missing something here ...

 

[-pari-]

definately weird. i shall redo/ask around with that question and get back. in the meantime, another question has popped up!

(1) Mr and Mrs Jones mortage their house for $50 000. find the amount of the monthly repayments they will have to make if the mortgage is over 25yrs, if the interest on the mortgage is 14% p.a.

i keep getting: $598.82

answer says $601.88

got an inkling that the textbook answer might be wrong? what do you guys get?

[EDIT: actually just got the right answer. nvm, i was wrong ]

 

[-pari-]

Ross borrows $6000 and agrees to repay the loan and interst in 16 equal quarterly installments. the interest is 8% p.a and is calculuated quarterly on the balance owing.

a) find the amount of each quarterly installment - THIS part i was cool with, no probs,

b)find the simple interest rate which is equivalent to the interest rate used in the calculation above.

couldn't get part b...?
answer is 4.46%

2) Evaluate the sum of the first 20 terms of the series:
3 + 5 + 9 + 17 + 33 + 65....

 

[SoulSearcher]

Ignore.

 

[pLuvia]

Off topic:

Damn SS you are already on 4.5k posts, hypocritically speaking

On topic:

SS you are wrong there, the d doesn't equal to 2

 

[SoulSearcher]

My mistake, fuck I'm forgetting this stuff.

Well, the first term is T₁ = 3.
The second term is T₂ = T₁ + 2.
The third term is T₃ = T₂ + 4.
The fourth term is T₄ = T₃ + 8.
...
The 20th term would be T₂₀ = T₁₉ + 2¹⁹

I suppose the best thing to do here is to split the terms, sum up the powers of 2 and the T_n sequence, then add together. I just can't figure out how at the moment, and probably I'm forgetting a much easier method.

 

[stewbacca]

definately weird. i shall redo/ask around with that question and get back. in the meantime, another question has popped up!

(1) Mr and Mrs Jones mortage their house for $50 000. find the amount of the monthly repayments they will have to make if the mortgage is over 25yrs, if the interest on the mortgage is 14% p.a.

i keep getting: $598.82

answer says $601.88

got an inkling that the textbook answer might be wrong? what do you guys get?

[EDIT: actually just got the right answer. nvm, i was wrong ]

hate dumb questions lie tis where u need to put in eap of te little numbers to get the right answer.

 

[-pari-]

^ oh right!

can someone plz just check the answer for this one...

1) a paintin appreciated 16%p.a. it's currently $20 000. how long will it take for it to be worth $50 000

i keep getting approx. 7.2 yrs, but the answer says 6.2 years?

and am totally stuck on:

2) a plant grows s that it increases its height each month by 0.2 of its previous month's height. if it grows to 3m, find its height in the first month

3)
4
(sum symbol) 3n + 2
n=1

answer: 128...


but i can't get 'r' as a constant?

any help would be great

 

[-pari-]

*bump*

 

[-pari-]

:wave:

i got this question:

Barabara borrows $120 000 to be repaid over a period of 25 yrs at 6% per annum REDUCIBLE interest. Each yr there are K regular repayments of $F. interest is calculated and charged just before each repayment

what i dont get is...
with compound interest...we add 1 to the interest rate (ie, 0.06 becomes 1.06) becoz the interest is....well....the previous amounts PLUS the current amounts' interest - if that makes sense

according to the answer for this Q, you'd still add 1 so it becomes 1+(0.06/k)

but then...i dont get it coz...what significance does the "REDUCIBLE" have there?

 

[kokodamonkey]

i think they mean reducible as your only charged interest on the amount owing..

in terms of K... if its 6% p.a thats the same as 0.06. but if your paying bianually, you cahnge it to 3% (0.03) . do you get that? because its happening twice.. 0.06/2 = 0.03.. so what it means if you have k times a year then you are paying 0.06/k
does that make sense?