Question
Quantity I. In what time will Rs. 48,000 amount to Rs.
52,920 @ 5% compound interest? Quantity II. In what time will Rs. 50,000 amount to Rs. 53060.40 @ 4% compound interest payable half-yearly? Study the following information carefully and answer the Questions given below:Solution
Quantity I. A= P[1+ R/100]t ⇒ 52,920 = 48,000 [1+ 5/100]t ⇒ 52,920/48,000 = [ 21/20]t ⇒ 441/400 = [ 21/20]t ⇒ [ 21/20]2 = [ 21/20]t ∴ t= 2 years Quantity II. Since interest is compounded half-yearly, R =4/2=2% p.a. and T =2xt = 2t years A= P[1+ R/100]t⇒ 53060.40 = 50,000[1+ 2/100]2t ⇒ 53060.40/50,000 = [ 102/100]2t ⇒ [ 51/50]3 = [ 51/50]2t ⇒2t = 3 yrs ∴ t = 3/2 years Hence Quantity I > Quantity II
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