Question

a sum of Rs 2000 becomes Rs 2315.25 after sometime at 5 percent per annum at compound interest. find the time


reply fast there is my maths unit test tomorrow

Answer 1

A/P=[(r+100)/100]^n
Where n= time
A=amount =2315.25
P=2000

R=5%
Put value and enjoy

Answer 2

Answer:

The time taken will be 3 years

Solution:

Given, the Principle (P) = Rs 2000

Amount (A) = Rs 2315.25

Rate (r) = 5%

Let the time be t.

Compound Interest is the interest compounded annually, bi-annually or quarterly at a certain rate of interest.

In comparison to Simple Interest which is calculated as a product of Principle, Rate and Time divided by 100.

Compound Interest can be calculated from the difference from the Amount that resulted after interest is compounded and the Principle.

The Amount for a Compound Interest can be calculated as:

$\begin{array} { c } { A = P \left( 1 + \frac { r } { 100 } \right) ^ { t } } \\\\ { R s 2315.25 = R s 2000 \left( 1 + \frac { 5 } { 100 } \right) ^ { t } } \\\\ { \frac { R s 2315.25 } { R s 2000 } = \left( \frac { 100 + 5 } { 100 } \right) ^ { t } } \\\\ { \quad \frac { 231525 } { 200000 } = \left( \frac { 105 } { 100 } \right) ^ { t } } \end{array}$

$\begin{aligned} \frac { 231525 } { 200000 } & = \left( \frac { 21 } { 20 } \right) ^ { t } \\\\ \frac { 9261 } { 8000 } & = \left( \frac { 21 } { 20 } \right) ^ { t } \\\\ \left( \frac { 21 } { 20 } \right) ^ { t } & = \left( \frac { 21 } { 20 } \right) ^ { 3 } \\\\ t & = 3 \end{aligned}$

Hence, time taken is 3 years.