Question

Find the sum of money that amounts to 5,850 in six years at 5% per annum.​

Answer 1

Step-by-step explanation:

let the principal be x

$interest = (x \times 5 \times 6 ) \div 100 \\ = \frac{30x}{100} \\ amount = x + \frac{30x}{100} \\ 5850 = \frac{100x + 30x}{100} \\ 585000 = 130x \\ x = 585000 \div 130 \\ x = 4500$

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Answer 2

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.