Mr A invests a certain sum of money for 3 years at simple rate of interest p.a. which fetches an interest on Rs 225.Mr B invests the same sum of money for 2 years at a compound rate of interest which is equal to the rate at which Mr. A invests.Mr B earns Rs 153 by way of interest.find the sum of money and the common rate of interest.
Answers
Given : Mr A invests a certain sum of money for 3 years at simple rate of interest p.a. which fetches an interest on Rs 225.
Mr B invests the same sum of money for 2 years at same rate but compounded annually and earn Rs 153 as interest
To Find : the sum of money and the common rate of interest.
Solution:
A different Approach :
Interest Earned in 3 Years = 225 Rs
=> Interest Earned in 1 Year = 75 Rs
1st Year interest will be same in both cases
Hence interest earned in 2nd year in case of compound interest
= 153 - 75 = 78 Rs
78 = 75 + 3 Rs
3 Rs additional interest is because of interest of Rs 75 earned in 1st Year
3 = 75 * R * 1/ 100
=> R = 4
Rate of interest = 4 %
75 = P * 4 * 1 /100
=> P = 7500/4
=> P = 1,875
sum of money = Rs 1875
the common rate of interest = 4 % per annum
Normal Approach
Amount = P
Rate of interest = R
225 = P * R * 3 /100
=> PR = 7500
153 = P (1 + R/100)² - P
=> 153 = P ( 1 + R²/10000 + 2R/100) - P
=> 1530000 = 10000P + PR² + 200PR - 10000P
=> 1530000 = PR² + 200PR
=> 1530000 = PR(R + 200)
=> 1530000 = 7500 (R + 200)
=> 204 = R + 200
=> R = 4
PR = 7500
=> P (4) = 7500
=> P = 1875
sum of money = Rs 1875
the common rate of interest = 4 % per annum
Learn More:
a certain sum of money is invested at a certain fix rate compounded ...
https://brainly.in/question/8524674
mr valia invested some money at a certain rate of simple interest per ...
https://brainly.in/question/9193066