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# A man deposits Rs.8,000 in a bank for 3 years at 5 % per annum compound interest. After 3 years he will get it.

Last updated date: 21st Feb 2024
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Hint: In this question principal amount is given , time is given , rate of interest is given . We have to find the amount after the time . We already know the formula for amount after time ‘t’.
A = $P{\left( {1 + \dfrac{R}{{100}}} \right)^t}$
Where ,
P = Principal amount
R = rate of interest
t = time
We have to substitute the value in the question in the formula mentioned and find the amount after 3 years. Let us try it !!!

Complete step-by-step solution:
In the the question given,
P = Principal amount = Rs.8,000
R = rate of interest = 5 % per annum
t = time = 3 years
Amount after 3 years A = $P{\left( {1 + \dfrac{R}{{100}}} \right)^t}$
$= 8000{\left( {1 + \dfrac{5}{{100}}} \right)^3} \\ = 8000{\left( {\dfrac{{100 + 5}}{{100}}} \right)^3} \\ = 8000{\left( {\dfrac{{105}}{{100}}} \right)^3} \\ = 9261$
Hence money after 3 years for principal amount Rs.8000 , rate of interest is 5% per annum is Rs.9,261 .

Note: The concept of interest is in use vastly nowadays . If the interest rates vary by different year by year. The total amount is given by
A=$P\left( {1 + \dfrac{{{r_1}}}{{100}}} \right)\left( {1 + \dfrac{{{r_2}}}{{100}}} \right)...........$ for shortcut methods . But the interest is calculated year by year for better understanding. There is another process for this problem. Alternatively , That method is to calculate interest year by year and summing up. The amount calculated in first year is taken as principal amount and second year so on .