Find the compound interest on Rs 25000 for one year at 8% p.a. compounded quarterly

Find the amount and the compound interest on the following :
Rs.25000 for 2 years at 6% per annum compounded semi-annually.

Solution

Rs.25000 for 2 years at 6% per annum compounded semi-annually.
Here P = Rs.25000, t = 2 years, r = 6%
Since interest is compounded semi-annually, so
Amount
= `"P"(1 + "r"/200)^(2"t")`

= `25000(1 + 6/200)^4`

= `25000(103/100)^4`
= 28137.72
Hence, Amount = Rs.28137.72
Also, C.I.
= A - P
= Rs.28137.72 - Rs.25000
= Rs.3137.72.

Concept: Concept of Compound Interest - When the Interest is Compounded Half Yearly

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Answer

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Hint: Calculate the compound interest for the first year, then for the second year and finally for the third year. Since the interest is compounded annually, the interest at the end of each year will be added to the total amount over which the interest will be calculated for the next year. Use $S.I=\dfrac{P\times r\times t}{100}$.

Complete step-by-step answer:

When interest on a certain sum is compounded annually, the interest at the end of each year is added to the total amount over which the interest is calculated for the next year.
Here we have for the first year P = 25,000, r = 20%,t =1 year.
Using $S.I=\dfrac{P\times r\times t}{100}$, we get
Interest for the first year $=\dfrac{25000\times 20}{100}=5000$
Hence P for second year = 25000+5000 = 30000, r= 20% and t = 1 year
Using $S.I=\dfrac{P\times r\times t}{100}$, we get
Interest for the second year $=\dfrac{30000\times 20}{100}=6000$
Hence P for third year = 30000+6000 = 36,000, r= 20% and t = 1year.
Using $S.I=\dfrac{P\times r\times t}{100}$, we get
Interest for the third year $=\dfrac{36000\times 20\times 1}{100}=7200$
Hence the interest for the third year = Rs 7200
Hence option [b] is correct.

Note: Alternatively we know for a sum compounded annually
${{A}_{n}}=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$ and ${{I}_{n}}={{A}_{n}}-{{A}_{n-1}}$ where ${{A}_{n}}$ is the amount at the end of the nth year and ${{I}_{n}}$is interest for the nth year.
Using, we get
$\begin{align}
& {{I}_{3}}=P{{\left( 1+\dfrac{r}{100} \right)}^{3}}-P{{\left( 1+\dfrac{r}{100} \right)}^{2}} \\
& =25000{{\left( 1.2 \right)}^{3}}-25000{{\left( 1.2 \right)}^{2}} \\
& =43200-36000=7200 \\
\end{align}$
Hence interest for the third year = Rs 7200, which is same as obtained above.

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Simple Interest And Compound Interest

A sum of Rs. 25000 invested a...

Updated On: 27-06-2022

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12 yr 1 yr `1(1)/(2)` yr None of these

Answer : C

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