A man deposited Rs.10000 in a bank with an interest rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the amount after 20 years.
Last updated date: 26th Mar 2023
•
Total views: 308.4k
•
Views today: 5.85k
Answer
308.4k+ views
Hint: Initially find the interest of the first year by using the given data. And by using the interest we can also find the amount that has been deposited in the 15th year and this helps to calculate the amount after 20 years.
Complete step by step answer:
Here from the data it is given that a man deposited Rs.10000 in a bank with an interest rate of 5% simple interest annually.
So, it is known that in simple interest, the interest remains the same in all years.
This means if we find interest in the first year then the interest will be the same for all years.
Now let us find interest for first year
$I = PTR$
Here I is the interest, P= Rs.10000, R=5% and t=1(for one year)
$\begin{gathered}
\Rightarrow I = 10000 \times 5\% \times 1 \\
\Rightarrow I = 10000 \times \dfrac{5}{{100}} \\
\Rightarrow I = 500 \\
\end{gathered} $
So interest of first year =Rs.500
Therefore interest for all years is also Rs.500 as it is simple interest used by the person.
Hence,
Amount in 1st year=Rs.10000
Amount in 2nd year = Amount in 1st year +Interest = Rs.10000 + Rs.500 =Rs.10500
Amount in 3rd year = Amount in 2nd year + Interest = Rs10500 + Rs.500 =Rs.11000
Hence our series is
Rs.10000, Rs.10500, Rs.11000 …
If we observe the series it is of AP
Where a=10000 and d=500 (interest is 500 which is common for all years)
Or else d=a2-a1 which implies d=10500-10000=500
There d=500
Now here we need to find amount in 15th year, as the series are in AP let us use nth term of AP where n=15
So, nth term of AP
$ \Rightarrow {a_n} = a + (n - 1)d$
Amount in 15th year = $a + (n - 1)d$
=10000 + (15-1)500
=10000+14(500)
=17000
Therefore amount in 15th year is Rs.17000
And also here we need to find amount after 20 year
i.e. we need to calculate ${a_n}$ value where n=21
Amount after 20 year = ${a_n}$
= $a + (n - 1)d$
=10000 + (20-1)500
=10000+19(500)
=20,000
Therefore amount after 20 years is Rs. 20,000.
Note: As the person has taken simple interest, so for every year the interest will be the same .So find interest for 1st year which will be the same for all other years. Later adding interest to the previous year amount we get the present year amount. As interest is common the amount will be in AP series. Make a note that the series is of AP so we have used the nth term of AP formula to find amount for 15th year and amount after 20 years.
Complete step by step answer:
Here from the data it is given that a man deposited Rs.10000 in a bank with an interest rate of 5% simple interest annually.
So, it is known that in simple interest, the interest remains the same in all years.
This means if we find interest in the first year then the interest will be the same for all years.
Now let us find interest for first year
$I = PTR$
Here I is the interest, P= Rs.10000, R=5% and t=1(for one year)
$\begin{gathered}
\Rightarrow I = 10000 \times 5\% \times 1 \\
\Rightarrow I = 10000 \times \dfrac{5}{{100}} \\
\Rightarrow I = 500 \\
\end{gathered} $
So interest of first year =Rs.500
Therefore interest for all years is also Rs.500 as it is simple interest used by the person.
Hence,
Amount in 1st year=Rs.10000
Amount in 2nd year = Amount in 1st year +Interest = Rs.10000 + Rs.500 =Rs.10500
Amount in 3rd year = Amount in 2nd year + Interest = Rs10500 + Rs.500 =Rs.11000
Hence our series is
Rs.10000, Rs.10500, Rs.11000 …
If we observe the series it is of AP
Where a=10000 and d=500 (interest is 500 which is common for all years)
Or else d=a2-a1 which implies d=10500-10000=500
There d=500
Now here we need to find amount in 15th year, as the series are in AP let us use nth term of AP where n=15
So, nth term of AP
$ \Rightarrow {a_n} = a + (n - 1)d$
Amount in 15th year = $a + (n - 1)d$
=10000 + (15-1)500
=10000+14(500)
=17000
Therefore amount in 15th year is Rs.17000
And also here we need to find amount after 20 year
i.e. we need to calculate ${a_n}$ value where n=21
Amount after 20 year = ${a_n}$
= $a + (n - 1)d$
=10000 + (20-1)500
=10000+19(500)
=20,000
Therefore amount after 20 years is Rs. 20,000.
Note: As the person has taken simple interest, so for every year the interest will be the same .So find interest for 1st year which will be the same for all other years. Later adding interest to the previous year amount we get the present year amount. As interest is common the amount will be in AP series. Make a note that the series is of AP so we have used the nth term of AP formula to find amount for 15th year and amount after 20 years.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
