# A Sum of Money Placed at Compound Interest Compounded Annually Amounts to Rs 47,610 in 2 Years and to Rs 54,751.50 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 47,610 in 2 years and to Rs 54,751.50 in 3 years. Calculate the rate of interest and the sum.

#### Solution

P = x ; r =? ; t= 2 and 3 years ; A= Rs 47,610 (2 years) (3 years)

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

47610 = x (1 + "r"/100)^2 ..........(i)

54751.50 = x (1 + "r"/100)^3  ................(ii)

 therefore ("x" (1 + "r"/100)^3)/("x" (1 + "r"/100)^2) =54751.50/47610

⇒(1 + "r"/100) = 54751.50/47610

⇒ "r"/100 = 54751.50/47610 - 1

⇒ "r"/100 = (54751.50 - 47610)/47610

"r" = 7141.50/47610 xx 100

r = 15 %

Using (i)

"x" (1 + "r"/100)^2 =" Rs"  47610

"x" (1 + 15/100)^2 = "Rs"  47610

"x" (115/100)^2= Rs 47610

1.3225 x = Rs 47,610

x = Rs 36,000

The sum =Rs 36,000 and rate of interest= 15 %

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#### APPEARS IN

Frank ICSE Class 10 Mathematics Part 2
Chapter 1 Compound Interest
Exercise 1.6 | Q 22 | Page 20