Find the sum of money that amounts to 5,850 in six years at 5% per annum.
Answers
7605 is the answer
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GIVEN
The Time Period of Interest(T) = 6yrs
The Rate of Intrest per Annum (R) = 5%
The Amount (A) have to return at end of 6yrs is Rs.5,850
TO FIND :- The Principal or Sum of money taken as Intrest.
FORMULA TO BE USED
Simple Intrest =
Simple Intrest =[Principal × Rate × Time(yrs)]/100
Amount = Principal + Simple Intrest
SOLUTION
Let the Principal be "p".
Now,
S.I. = (P × R × T)/100 ... eq.01
Again, Amount = S.I. + Principal
=> S.I. = Amount - Principal ...eq.02
Equating Eq.01 and Eq.02,
=> (P × R × T)/100 = A - P
=> (P × 5 × 6)/100 = 5850 - P
=> 30P/100 = 5850 - P
=> 3P/10 = 5850 - P
=> 3P/10 + P = 5850
=> (3P + 10P)/10 = 5850
=> 13P/10 = 5850
=> 13P = 58500
=> P = 58500/13
=> P = 4500
Therefore, the Sum of money that used as Principal is Rs.4500. (ANS)
VERIFICATION
The Intrest by Formula 01 will be :-
P×R×T/100 = 4500 × 5 × 6 /100
= 45 × 30
= Rs.1350
Again, Intrest by Foruma 02 will be :-
Amount - P = 5850 - 4500
= Rs.I350
As Both the equations satisfy the condition, our solution is correct.