Arithmetic and Geometrical Progression
Hey everyone, looking for some more help / advice :)
Questions first, my answers at the bottom :)
Question One
The value of a machine which costs £35000 depreciates by 10% per annum.
A) What is its value after 10 years?
The costs of repairs and maintenance is £2000 in the first year and increases by 10% per year.
b) After how many years will it be cheaper to buy a new machine than to pay for the repairs and maintenance up till then?
Question Two
A man wishes to replay a debt of £3000 by paying a fixed sum of £60 per month to reduce the debt, together with a payment of 1% interest for that month indebtedness. Make a schedule of payment and find the total interest pain until the debt is completely discharged.
Question Three
A man deposits £1000 every year into a pension fund earning 6% interest per annum, compounded yearly. Deposits are made at the start of each year. How much will the fund be woth at the end of 15 years after the initial deposit?
My Answers (50% marking)
Q1 a- Calculated the long way of reducing the value by 10% for 10 years, value after 10 years = £12203.7454
b - 2000 * 1.1^30 = £34898.80454
2000 * 1.1^31 = £38388.68499
so, it will be cheaper to buy a new machine after 30 years.
Question Two - There are 50 "£60's" in £3000 so N= 50, D= 0.6, A= 0.6.
Sn= N/2*[(2A+(n-1)*d]
= 50/2*[2*0.6+(50-1)*0.6]
= 25*[1.2+(49*0.6)]
= 25*(1.2+29.4)
= 765
Question Three - Again calculated the long and painful way of adding 6% to the initial year and for each year thereafter adding £1000 then the 6%. Totaling a value of £24672.52808 after 15 years.
Comment on ArcSine's post
Hi, thank you very much for the reply!
I'm not sure if I'm just being slow here or not, but how can I then solve the issue in 1b? If I'm misreading your reply, I apologise and would be grateful if you point me toward the right direction :S
Comment on ArcSine's post
Ah, I understand now - apologies for my slowness lol! The wording is a bit of a mystery with most questions we get I'm afraid as English is not the lecturer's native language so it can get confusing.
Thank you very much for your help again!