Advertisement Remove all ads

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.

Advertisement Remove all ads

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 %

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Frank ICSE Class 10 Mathematics Part 2
Chapter 1 Compound Interest
Exercise 1.6 | Q 22 | Page 20
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×