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In what time will compound interest at 15% pa be greater than simple interest at 30% pa for the saame principal

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CA = P ( 1 + 0.15 )^n total sum at compound interest

Compound interest CI = CA - P

SA = P (1 + n 0.30) total sum at simple interest

Simple interest = SI = P n 0.30

CI = SI when

P[ (1.15)^n - 1 ] = P n 0.30 => 1.15^n = 1 + 0.3 n

1.15^9 < 3.7 but 1.15^10 > 4

=> ANSWER nearly 10 years

Compound interest CI = CA - P

SA = P (1 + n 0.30) total sum at simple interest

Simple interest = SI = P n 0.30

CI = SI when

P[ (1.15)^n - 1 ] = P n 0.30 => 1.15^n = 1 + 0.3 n

1.15^9 < 3.7 but 1.15^10 > 4

=> ANSWER nearly 10 years