# the simple interest on a certain sum of money for 2 years at 4 1/2% P. a is rs. 5400.what will be the compound interest on that s

the simple interest on a certain sum of money for 2 years at 4 1/2% P. a is rs. 5400.what will be the compound interest on that sum at the same rate for the same time period, if the interest is compounded annually.

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Step-by-step explanation:

Simple interest = Principal x time x rate

⇒ Rs.5400 = (Principal x 2 x  4  1/2) /100

⇒ Rs.5400 =( Principal x 2 x  9/2 )/100

⇒Rs.5400 = (Principal x9)   /100

⇒ Rs. 5400 x 100 = Principal x 9

⇒ Rs.540000 = Principal x 9

⇒ Rs.540000 / 9 = Principal

⇒ Principal = Rs.60,000

Compound interest = P [ 1 + R/100 ] power n

= 60,000 [ 1 + (9/2) /100] power 2

= 60,000 [ 1 + 9/200]²

= 60,000 [ 200/200 + 9/200]²

= 60,000 [ 209 / 200]²

= 60,000 x (209 / 200) x (209/ 200)

= (60,000 x 209 x 209 ) / 200 x 200

= 6 x 209 x 209 / 4

= 3 x 209 x209 / 2

= 65521.5