Question

The difference between compound interest and simple interest on a certain sum for 3 years at 5% per annum is 80 rupees. Find the sum

Answer 1

sum is Rs 10,491.80

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Answer 2

For the sum  of Rs 10491.8  the difference between compound interest and simple interest  for 3 years at 5% per annum is rupees 80

Given :

• The difference between compound interest and simple interest is Rs 80
• Rate of Interest is 5 % p.a.
• Time is 3 years

To Find :

• Sum invested

Step 1 :

Assume that Sum invested is  Rs  x

Step 2 :  

Apply Simple interest (SI) formula

SI = P * R * T /100

Step 3 :

Substitute the values to find Simple interest

SI =  x * 5 * 3/100

SI = 0.15x  Rs

Step 4 :

Apply formula for compound interest

$CI=P(1+\frac{R}{100})^T-P$

Step 5:

Substitute the values to find CI

$CI= x(1+\frac{5}{100})^3-100$

CI=0.157625x

Step 6 :

Find the Difference between CI and SI

15.7625x - 15x  = 0.007625x

Step 7 :

Equate the difference with given Difference Rs 80

0.007625x = 80

Step 8:

Solve for x

x ≈ 104.918

For the sum  of about Rs 10491.8  the difference between compound interest and simple interest  for 3 years at 5% per annum is rupees 80