English

A Certain Sum of Money Invested at Compound Interest Compounded Annually Amounted to Rs 5,082 After 2 Years and to Rs 5,590.20 After 3 Years. Calculate the Rate of Interest and the Sum Invested. - Mathematics

Advertisements
Advertisements

Question

A certain sum of money invested at compound interest compounded annually amounted to Rs 5,082 after 2 years and to Rs 5,590.20 after 3 years. Calculate the rate of interest and the sum invested.

Sum
Advertisements

Solution

Here, r =? P = x (say) 

T = 2 years and 3 years 

A= Rs 5,082 in 2 years and Rs 5,590.20 in 3 years. 

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

`5082 = "x" (1 + "r"/100)^2 ` ..................   (i)

`5590.20 = "x" (1 + "r"/100)^3` ................(ii)

Dividing (ii) by (i)

`("x"  (1 + "r"/100)^3)/("x" (1 + "r"/100)^2) = 5590.20/5082` 

`=> 1 + "r"/100 = 5590.20/5082`

`=> "r"/100 = 5590.20/5082 - 1`

`=> "r"/100 = (5590.20 - 5082)/5082`

`=> "r"/100 = 508.20/5082`

`=> "r" = 508.20/5082 xx 100`

⇒ r = 10%

using (i)

`"x" (1 + "r"/100)^2 = "Rs"  5082`

`"x" (1 + 10/100)^2 = "Rs"  5082`

`"x" xx 11/10 xx 11/10 = "Rs"  5082`

`"x" xx 121/100  = "Rs"  5082`

`"x" = "Rs"  (5082 xx 100)/121`

x = Rs 4200

Hence, rate of interest= 10°10 and sum invested =Rs 4,200. 

shaalaa.com
Use of Formula
  Is there an error in this question or solution?
Chapter 1: Compound Interest - Exercise 1.4 [Page 13]

APPEARS IN

Frank Mathematics - Part 2 [English] Class 10 ICSE
Chapter 1 Compound Interest
Exercise 1.4 | Q 5 | Page 13

RELATED QUESTIONS

Shekhar had a fixed deposit of Rs 24000 for 3 years . If he received interest at 10% p.a compounded annually, find the amount received by him at the time of maturity.


Rajeev borrowed Rs 15,000 from Sanjay at 12% p.a. compound interest. After 2 years Rajeev gave Rs 7,500 and a scooter to clear the account. Find the cost of the scooter.


The cost of a scooter depreciated by Rs 5100 during the second year and by Rs 4,335 during the third year. Calculate

The original cost of the scooter.


The cost of a machine depreciated by Rs 2592 during the third year and by Rs 2332.80 during the fourth year. Calculate :

The rate of depreciation.


The cost of a machine depreciated by Rs 2592 during the third year and by Rs 2332.80 during the fourth year. Calculate :

The original cost. 


Ramesh borrowed Rs 12,000 at 15% compound interest for 2 years. At the end of the first year he returned some amount and on paying Rs 9,200 at the end of the second year, he cleared the loan. Calculate the amount of money Ramesh returned at the end of the first year.


What sum of money will amount to Rs 10,256.40 in 3 years at compound interest if the rates of interest for the successive years are 10%, 11% and 12%?


Calculate the rate per cent at which Rs 16,000 will yield Rs 3,876.75 as compound interest in 3 years.


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.


If the interest is compounded half yearly, calculate the amount when the Principal is Rs. 7,400, the rate of interest is 5% per annum and the duration is one year.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×