Question

(b) An annuity wl pay £4,000 at the end of the year, for each of the next three years. At an interest rate of 6%, fid the present value of the annuity. (5 marks) (c)A machine is bought for £120,000 and its value depreciates at a constant rate. After two years its value is £90,000. i. What is the annual rate of depreciation? (2 marks) ii. A second machine, also costing £120,000, depreciates at 20% each year (You may use the facts that, to three decimal places, log 0.5-0.301 and (3 marks) After how many years will it be worth £60,000? log 0.8-0.097.)

Answer 1

b) annuity value after 1 year= 4000

rate 6%

time 3 years

present value= 4000/(1.06)³= 3361 approx.

c) value of machine today= 120000

after 2 years = 90000

total depreciation= 120000-90000= 30000

depreciation for year= 30000/2=15000

rate of depreciation= 15000/120000=12.5%

(ii) cost of machine= 120000

rate = 20%

ist year depreciation= 120000*20%=24000

iind year deprecuation = 24000

remaining value after 2 years= 120000-24000-24000=72000

now 72000* 20%×t/12=12000(72000-60000)

=10 month

Therefore in in 2 year and 10 month ,the amount will become 60000.