Question

The difference between Simple and Compound Interest for a certain sum of money for 3 years at 5% per anum is rupees 61. Find the principal.
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Answer 1

Given,

C.I - S.I = Rs. 61

Rate = 5%

Time = 3 years

P = ?

Suppose,

P = Rs. 100

So,

S.I = (P × R × T)/100

S.I = (100 × 5 × 3)/100

S.I = 5 × 3

S.I = Rs. 15

&

C.I

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

C.I

$= 100 {( \frac{105}{100} )}^{3} - 100$

C.I

$= 100 {( \frac{21}{20} )}^{3} - 100$

C.I

$= 100( \frac{9261}{8000} ) - 100$

C.I

$= ( \frac{9261}{80} ) - 100$

C.I

$= ( \frac{9261 - 8000}{80})$

C.I

$= ( \frac{1261}{80} )$

C.I = Rs. 15.7625

Difference = C.I - S.I = 15.7625 - 15 = 0.7625

Main difference = Rs. 61

So,

Principal (P) = (P × 61)/0.7625

P = (100 × 61)/0.7625

P = 6100/0.7625

P = Rs. 8000

The Main Principle (P) = Rs. 8000