Question

Find the time taken in years for Rs.20000 to
earn an interest of Rs.5194 at 3% interest,
compounded annually.
​

Answer 1

Given:

• Principal = Rs. 20000
• Interest = Rs. 5194
• Rate = 3%

To find:

• Time in years?

Solution:

★ Finding amount,

➻ Amount = Principal + Interest

➻ 20000 + 5194

➻ Rs 25194

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

★ Now, Finding time using the formula,

We know that,

★ A = P(1 + r/100)^n

Therefore,

➻ 25194 = 20000(1 + 3/100)^n

➻ 25194 = 20000(1 + 0.03)^n

➻ 25194 = 20000(1.03)^n

➻ 25194 = 20000(1.03)^n

➻ 25194/20600 = (1.03)^n

➻ 1.22300 = (1.03)^n

➻ n = log(1.22300)/log(1.03)

➻ n = 6.810

➻ n = 6.8 years (approx)

∴ Hence, Time taken for Rs. 20000 to earn an interest of Rs. 5194 is 6.8 years.

Answer 2

Given :-

Rs. 20000 is invested compounded annually at a rate of 3% to get a Interest of Rs. 5194 .

To Find :-

The time taken to have a Interest of Rs. 5194 at a rate of 3% on Rs. 20000.

Used Concepts :-

• A = P + C.I , where ( A ) is amount , ( P ) is principal and ( C.I ) is Compound Interest.
• The Formulae of Amount i.e A = P × ( 1 + R/100 )^ t , where ( A ) is final amount , ( P ) is principal , ( R ) is Rate of Interest and ( t ) is Time Taken .
• If base of two powers is same where power is not same . Then power is also same .

Solution :-

Here , Principal ( P ) = Rs. 20000

Time taken ( t ) = ?

Rate of Interest ( R ) = 3% compounded annually

Compound Interest ( C.I ) = Rs. 5194

Now , Amount ( A ) = P + C.I

A = 20000+ 5194

A = 25194

Therefore , The total amount is Rs. 25194 .

Now , Putting all values in A = P × ( 1 + R/100)^ t.

25194 = 20000 × ( 1 + 3/100)^t

25194 = 20000 × ( 103/100 )^ t

25194 = 20000 × ( 1.03 )^ t

( 1.03 )^ t = 25194/20000

( 1.03 )^ t = 1.2597

( 1.03 )^ t = ( 1.03 )^ 1.22

Now the base of both powers is same . So Here,

t = 1.22 ( approx ) .

Hence , The required time is 1.22 years .