Question

Mahi borrowed a certain sum for 2 years at simple interest from Priti Mahil and the sum to Rathna at same rate for 2 years compounded annually at the end of 2 years Mahi received rupees 205 as compound interest but paid 200 rupees at simple interest find the sum​

Answer 1

Answer:

The sum of money borrowed by Mahi is Rupees 500.

Step-by-step explanation:

Le the amount be P.

Simple interest = Principle × i × 2

Compound interest = P(1 + i)² - P

i = interest rate

p = the principal

Substituting the values we have:

2Pi = 200

Pi = 100

P = 100/i

P(1 + i)² - P = 205

P[(1 + i)² - 1] = 205

P = 205/[(1 + i)² - 1]

Equating the two we have:

100/i = 205/[(1 + i)² - 1]

100[(1 + i)² - 1] = 205i

100(1 + i)² - 100 = 205i

100(1 + 2i + i²) - 100 = 205i

100 + 200i + 100i² - 100 = 205i

Collecting the like terms together we have:

100i²+ 200i - 205i = 0

100i² - 5i = 0

5i = 100i²

Diving both sides by 5i² we get:

i = 20%

The interest rate is 20%.

Let's now calculate the principal as follows:

200 = P × 20/100 × 2

0.4P = 200

P = 500

The sum of money borrowed by Mahi is Rupees 500.