Question

some money was lent on 4% compound interest if the difference of second and the first year is 88 find the principal​

Answer 1

principal = 55000

let principal is P.

rate of compound interest , r = 4%

it means interest on the first year = P(1 + r/100)¹ - P

= 4P/100 = 0.04P

given, compound interest for the second year = [P(1 + r/100)ⁿ - P ] - 0 04P

= [P(1 + 4/100)² - P] - 0.04P

= [P(1.04)² - P ] - 0.04P

= 1.0816P - P - 0.04P

= 0.0816P - 0.04P

= 0.0416 P

now difference of second and first year = 88 Rs.

or, 0.0416P - 0.04P = 88Rs

or, 0.0016P = 88

or, P = 88/0.0016 = 55000 Rs.

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Answer 2

Amount lent = Rs 55000  if difference of second and the first year interest  is Rs 88 at 4%

Step-by-step explanation:

A good solution already exist here

But A different Approach to solve

Difference in compound interest of 2nd year & 1st year is the interest earned in 2nd year on Amount of  Interest Earned in First Year

Using

Simple interest = P * R * T /100

88  = First Year Interest *  4  *  1 /100

=> First Year Interest = 2200

First Year interest = P * 4 * 1 /100

=> 2200 = P * 4 /100

=> P = 55000

Amount lent = Rs 55000

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