Question
A certain amount of money at r%, compounded annually after two and three years becomes Rs.1440 and Rs.1728 respectively. r is
Answer: Option A
Answer: (a)If the principal be Rs.P, thenA = P$(1 + R/100)^T$1440 = P$(1 + R/100)^2$ ...(i)and 1728 = P$(1 + R/100)^3$ ...(ii)On dividing equation (ii) by (i),$1728/1440 = 1 + r/100$$r/100 = 1728/1440$ - 1= ${1728 - 1440}/1440 = 288/1440$r = ${288 × 100}/1440$r = 20% per annumUsing Rule 7(i),Here, b - a = 3 - 2 = 1B = Rs.1728, A = Rs.1440R% = $(B/A - 1)$ × 100%= $(1728/1440 - 1) × 100%$= $({1728 - 1440}/1440) × 100%$= $[288/1440] × 100%$ = 20%
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Answer: (a)If the principal be Rs.P, thenA = P$(1 + R/100)^T$1440 = P$(1 + R/100)^2$ ...(i)and 1728 = P$(1 + R/100)^3$ ...(ii)On dividing equation (ii) by (i),$1728/1440 = 1 + r/100$$r/100 = 1728/1440$ - 1= ${1728 - 1440}/1440 = 288/1440$r = ${288 × 100}/1440$r = 20% per annumUsing Rule 7(i),Here, b - a = 3 - 2 = 1B = Rs.1728, A = Rs.1440R% = $(B/A - 1)$ × 100%= $(1728/1440 - 1) × 100%$= $({1728 - 1440}/1440) × 100%$= $[288/1440] × 100%$ = 20%
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