Question

In how many years will a sum of Rs.3000 amount to Rs.3630 at 10% pa compounded annually.

Answer 1

Answer:

Step-by-step explanation:

According to the question,

Principle = Rs 3000

Amount = Rs 3630

Rate = 10%.

Time = n.

We know the formula:

A = P$(1 + 0.01r)^{n}$

or, 3630 = 3000$(1 + 0.01*10)^{n}$

or, 1.21 = $(1.1)^{n}$

or, $(1.1)^{2}$ = $(1.1)^{n}$

or, n = 2. [Ans]

Therefore, a sum of Rs.3000 amount to Rs.3630 at 10% pa compounded annually in 2 years.

Answer 2

Solution :

Given Principal ( P ) = Rs 3000

Amount ( A ) = Rs 3630

Rate of interest ( r ) = 10% per annum

Number of times Interest paid = n

We know that ,

P( 1 + r/100 )ⁿ = A

=> ( 1 + r/100 )ⁿ = A/P

=> ( 1 + 10/100 )ⁿ = ( 3630/3000 )

=> ( 1 + 1/10 )ⁿ = ( 121/100 )

=> [( 10 + 1 )/10 ]ⁿ = ( 11/10 )²

=> ( 11/10 )ⁿ = ( 11/10 )²

=> n = 2

[ Since , a^m = a^n => m = n ]

Therefore ,

In 2 years the sum Rs 3000 amount

to Rs 3630 at 10% per annum

compounded annually.

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