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# Find the amount and the compound interest on Rs.$8000$ at $5$% per annum for $2$ years, compounded annually.

Last updated date: 21st Jul 2024
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Hint: First we have to define what the terms we need to solve the problem are.
This problem is of compound interest.
Simple interest is based on the principal amount of a loan or deposit whereas compound interest is based on the principal amount and the interest that accumulates on its every period.

Formula used:
$A = P \times {(\dfrac{{1 + R}}{{100}})^T}$
Where R is the annual rate of interest, T is number of years, P is the principal amount and
A will be the amount after T years.

Complete step by step solution:
Since we are going to use compound interest formula to solve this problem
That is $A = P \times {(\dfrac{{1 + R}}{{100}})^T}$
Where R is the annual rate of interest, T is number of years, P is the principal amount and
A will be the amount after T years.
As we know the principal amount is Rs.$8000$, the rate of interest is $5$% per annum which is$P = Rs.8000$, $R =$$5$% and $T = 2$years
So, substituting all the values in the compound interest formula we get
Amount = $P \times {(1 + \dfrac{R}{{100}})^T}$
$\Rightarrow 8000 \times {(1 + \dfrac{5}{{100}})^2}$
Simplifying further we get $8000 \times {(1.05)^2}$
$\Rightarrow 8820$
Hence the amount credited for two years will be equal to Rs. $8820$ and we need to find the compound interest for this amount
Thus, compound interest = Amount – Principal
That is $C.I = A - P$
$C.I = 8820 - 8000 = 820$
Therefore, the amount is $Rs.8820$ and the compound interest is $Rs.820$

Note: Simple interest and compound interest are not the same, Simple interest depends on principal amount of deposited and compound interest depends on interest that accumulate on every period
So, we have to put compound interest formula for this problem and If interest is compounded yearly, then $n = 1$ ; if semi-annually, then $n = 2$; quarterly, then $n = 4$; monthly, then $n = 12$; weekly, then $n = 52$; daily, then $n = 365$; and so forth, regardless of the number of years involved.
Also, "t" must be expressed in years, because interest rates are expressed that way.