13. A machine costs 5,20,000 with an estimated life of 25 years. A sinking fund is created to
replace it by a new model at 25% higher cost after 25 years with a scrap value realization
of 25000. what amount should be set aside every year if the sinking fund investments
accumulate at 3.5% compound interest p.a.?
(a) 16,000
(b) 16,500
(c) 16,050
(d) 16,005
Answers
Answer:
Given A machine costa 520000 with an estimated life of 25 yrs a sinking find is created replace it by a model at 25%higher cost after 25 yrs with a scrap value realize of 25000 what amount should be set aside every year if the sinking find investment accumulate at 3.5%compound interest p.a.?
Machine cost is Rs 5,20,000
After 25 years cost will be 5,20,000 x 125 / 100
= 6,50,000
Now scrap value is Rs 25,000
Therefore total money required will be 6,50,000 – 25,000
= 6,25,000
Let Rs a be invested every year.
a (103.5 / 100)^25 + a(103..5 / 100)^24 +------------+ a(103.5 / 100) = 6,25,000
a[1 + p + p^2 +--------------p^25] – a = 6,25000 where p = 103.5/100
a{[1 – p^25 + 1 / 1 – p] – 1 } = 625000
a[p – p^26 / 1- p] = 6,25,000
a = (1 – 1.035 / 1.035 – 2.3632)625000
= 16469.1
≅ 16500