# A Sum of Money Placed at Compound Interest Compounded Annually Amounts to Rs 31,360 in 2 Years and to Rs 35,123.20 in 3 Years. Calculate the Rate of Interest and the Sum. - Mathematics

Sum

A sum of money placed at compound interest compounded annually amounts to Rs 31,360 in 2 years and to Rs 35,123.20 in 3 years. Calculate the rate of interest and the sum.

#### Solution

P = x ; r = ? ; t= 2 and 3 years ; A = Rs 31,360 ( 2 years) and Rs 35, 123.20 ( 3 years)

"A" = "P" (1 + "r"/100)^"n"

31360 = x (1 + "r"/100)^2 .........(i)

35123.20 = "x" (1 + "r"/100)^3  ..............(ii)

therefore ("x" (1 + "r"/100)^3)/(x (1 + "r"/100)^2) = 35123.20/31360

⇒ (1 + "r"/100) = 35123.20/31360

⇒ "r"/100 = 35123.20/31360 - 1

⇒ "r"/100 = (35123.20 - 31360)/31360

"r" = 3763.20/31360 xx 100

r = 12%
Using (i)

"x" (1 + "r"/100)^2 = Rs 31,360

"x" (1 + 12/100)^2 = Rs 31,360

"x" (112/100)^2 = Rs 31,360

1 .2544 X = Rs 31,360

x = Rs 25,000

The sum = Rs 25,000 and rate of interest = 12 %.

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#### APPEARS IN

Frank ICSE Class 10 Mathematics Part 2
Chapter 1 Compound Interest
Exercise 1.6 | Q 23 | Page 20