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Question
Ashok invests a certain sum of money at 20% per annum, compounded yearly. Geeta invests an equal amount of money at the same rate of interest per annum compounded half-yearly. If Geeta gets Rs. 33 more than Ashok in 18 months, calculate the money invested.
Solution
(i) For Ashok (interest is compounded yearly) :
Let P = Rs. y; n = 18 months = `1 1/2` year and r = 20% p.a.
For 1 year
A = `"P"( 1 + r/100 )^n = y( 1 + 20/100 )^1 = (6/5)y`
For `1/2` year
P = Rs. `(6/5)y ; n = 1/2` year and r = 20%
A = `"P"( 1 + r/[2 xx100] )^(n xx 2) = Rs. (6/5)y ( 1 + 20/[ 2 xx 100])^(1/2 xx 2) = Rs. (66/50)y`
(ii) For Geeta ( interest is compounded half-yearly )
P = Rs. y ; n = `1 1/2` year and r = 20% p.a.
`"A" = "P"( 1 + r/[ 2 xx 100 ])^( n xx 2) = y( 1 + 20/[ 2 xx 100 ])^( 3/2 xx 2) = y( 11/10 )^3`
= Rs. `(1,331)/(1,000)y`
According to question
∴ `(1,331)/(1,000)y - ( 66/50 )y = Rs. 33`
= `( 11/(1,000))y = Rs. 33`
= y = Rs. `[ 33 xx 1,000 ]/11 = Rs. 3,000`
Money invested by each person=Rs. 3,000.
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