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1. How much money must set aside each ycar so as to replace a machine that will cost Rs.15,000 after 8 years? Therate of interest being 12% per year compounded

Answer»

If we insure a Principal amount of P at a compound interest at rate 'r' for a period of 'n' years, then principal along with interest would be equal to

= P(1+r)^n

But here, principal amount is insured every year for 8 years

Now, given r = 12%

For initial amt insured, P(1+r)^8

For amt insured after 1yr, P(1+r)^7

For amt insured after 2yr, P(1+r)^6

......so on till 8 yrs

So, total returns = P[(1+r)^8 + (1+r)^7 +.....+1 ] = 15000(given)

=>P[(1+r)^9-1]/r=15000 ( Sum to 9 terms of a G.P)

On simplification we get, P = 1017 Rs


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