a sum of rupees 2000 becomes rupees 2315.25 after sometime at 5% per annum at compound interest . find the time
Answers
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{lgathered}\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}\end{lgathered}
A=P(1+
100
r
)
t
Rs2315.25=Rs2000(1+
100
5
)
t
Rs2000
Rs2315.25
=(
100
100+5
)
t
200000
231525
=(
100
105
)
t
\begin{lgathered}\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}\end{lgathered}
200000
231525
8000
9261
(
20
21
)
t
t
=(
20
21
)
t
=(
20
21
)
t
=(
20
21
)
3
=3
Hence, time taken is 3 years.
Step-by-step explanation:
Hope it helps you
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{lgathered}\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}\end{lgathered}
A=P(1+
100
r
)
t
Rs2315.25=Rs2000(1+
100
5
)
t
Rs2000
Rs2315.25
=(
100
100+5
)
t
200000
231525
=(
100
105
)
t
\begin{lgathered}\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}\end{lgathered}
200000
231525
8000
9261
(
20
21
)
t
t
=(
20
21
)
t
=(
20
21
)
t
=(
20
21
)
3
=3
Hence, time taken is 3 years.
Step-by-step explanation:
Hope it helps you
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Step-by-step explanation: