What will be the amount after 1 year a sum of Rs 32000 at 20% per annum when the interest is compounded half yearly?

Sum

Find the amount and the compound interest on ₹ 32,000 for 1 year at 20% per annum compounded half-yearly.

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Solution

Principal (P) = ₹32,000

Time (t) = 1 year

Rate (r) = 20%

Amount =`"Principal"xx(1+"r"/(2xx100))^("n"xx2)`

`=₹32,000xx(1+20/200)^(1xx2)`

`=₹32,000xx(11/10)^2`

`=₹32,000xx11/10xx11/10`

= ₹38,720

C.I. = Amount − Principal

= ₹38,720 − ₹32,000

= ₹6,720

Concept: Interest Compounded Half Yearly

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Chapter 9: Interest - Exercise 9 (C) [Page 115]

Q 24Q 23Q 25

APPEARS IN

Selina Concise Mathematics Class 8 ICSE

Chapter 9 Interest
Exercise 9 (C) | Q 24 | Page 115

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Question

If the interest is compounded half-yearly, calculate the amount when the principal is  Rs7400, the rate of interest is 5% per annum and the duration is one year.

Hint:

From the information provided, use the formula of total amount.

The correct answer is: 7774.63 Rs

Complete step by step solution:We calculate the total amount by the formula …(i)where P is Principal amount, T is number of years and R is rate of interestHere, we have T = 1, P = 7400, R = 5% and A = ?On substituting the known values in (i), we get  Rupees which can be rounded to 7774.63 Rs

hi welcome to this video and depression is find the amount and the compound interest on rupees 32000 for one year at 20% per annum compounded half yearly fees of compounded half-yearly so first of all it is at a given conditions here so principal is equal to Rupees 32000 and rate of interest will be equal to Capital R by 2 because it is a case of component half yearly fee in case of component half yearly we always divide the rate for a no by to so this is equal to 20 over two letters 10% and also the value of can we get by multiplying the time period in years with two so this should be equal to 2 into 10 to the time period is one year sudasudi call to to write the formula of amount amount is equal to P in bracket

1 + power over 100 to the power and the given values for amount will be equal to 32000 in bracket 1 + are that is 10 over 100 to the path to have been cancelled these 20 and will get 32000 in bracket 11 by 10 into 11 by 10 now cancel these two zeros with these two zeros and finally you will get the value of amount is equal to 320 into 11 into 11 and that will give us rupees 38000 720 so this is the value of amount and from this value of amount we will calculate the value of compound interest compounded should be equal to amount - principal

after the values here will get 38720 -32000 so this rupees 6720 so this is the value of CL I hope you have understood thank you

Correct Answer - Option 1 : 38720

Given:

Principal = Rs. 32000

Rate of interest = 20%

Time = 1 year

Formula used:

A = P (1 + r/100)n

Where, A = Amount, P = Principal, n = Time, r = Rate of interest

Calculation:

When interest is compounded half yearly, then

R becomes 20%/2 = 10%  and T becomes 2T

A = P (1 + r/100)n

⇒ A = 32000 × (1 + 10/100)2

⇒ A = 32000 × (11/10) × (11/10)

⇒ A = 32000 × (121/100)

⇒ A = 38720.

∴ The amount is Rs. 38720.

Find the compound interest on Rs. $32000$ at $20\% $ per annum for $1$ year, compounded half yearly.(a) Rs. $6320$ (b) Rs. $6720$(c) Rs. $6400$ (d) Rs. $6500$

Answer

Verified

Hint:In this example, given that the rate of interest is annual and the interest is compounded half yearly (that is, six months). That means the interest paid at the end of every six months is one-half of the rate of interest per annum. So, the rate of annual interest is $\dfrac{R}{2}\% $ and the number of years is doubled (that is, $2T$). First we will find the amount $A$ for $1$ year by using the formula $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$. After that we will find compound interest by subtracting the principal amount $P$ from the amount $A$.

Complete step-by-step solution:
Here given that the principal amount $P = $ Rs. $32,000$, rate of interest $R = 20\% $ per annum and time $T = 1$ year. Also given that the interest is compounded half yearly (that is, six months). So, the interest paid at the end of every six months is one-half of the rate of interest per annum. So, the rate of annual interest is $R = \dfrac{{20}}{2}\% = 10\% $ and the number of years is doubled. That is, $T = 2$ half years.
Now we are going to find the amount for $1$ year by using the formula $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$ where $P$ is principal amount, $R$ is rate of annual interest and $T$ is time in half years.
Now we are going to substitute the values of $P$, $R$ and $T$ in the formula of amount for $1$ year.
Therefore, $A = 32000{\left( {1 + \dfrac{{10}}{{100}}} \right)^2}$
$ \Rightarrow $ $A = 32000{\left( {\dfrac{{100 + 10}}{{100}}} \right)^2}$
$ \Rightarrow $$A = 32000{\left( {\dfrac{{110}}{{100}}} \right)^2} = 32000{\left( {\dfrac{{11}}{{10}}} \right)^2} = 32000\left( {\dfrac{{121}}{{100}}} \right)$
$ \Rightarrow $ $A = 320 \times 121$ $ = $ Rs. $38720$
Now we will find compound interest by subtracting the principal amount $P$ from the amount $A$.
Therefore, compound interest (CI) $ = $ $A - P$
$ \Rightarrow $ Compound interest (CI) $ = $ $38720 - 32000$ $ = $ Rs. $6720$.

Therefore, the compound interest is Rs. $6720$ for $T = 1$ year.

Note:Simple interest is calculated only on the principal amount but compound interest is calculated on principal amount as well as previous year’s interest. If interest is paid only for $T = 1$ year then there is no distinction between simple interest and compound interest.

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