Find the compound interest on a sum of Rs 10000 for two years at 10 p.a. compounded half yearly

Sum

Find the compound interest on Rs.10000 for 2 years at 8% per annum compounded half-yearly.

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Solution

Principal P = ₹ 10,000

Rate of interest R = 8% p.a. compounded half-yearly

Duration T = 2 years

A = P`(1 + (("R"/2))/100)^"2T"`

= `10000(1 + (8/2)/100)^4`

= `10000(1 + 4/100)^4`

= 10000(1.04)4

= 11698.58

I = A – P

= 11648.58 – 10000

= 1698.58

∴ Compound interest is  ₹ 1698.58.

Concept: Simple and Compound Interest (Entrance Exam)

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Chapter 9: Commercial Mathematics - Exercise 9.3 [Page 130]

Q 5Q 4Q 6

APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board

Chapter 9 Commercial Mathematics
Exercise 9.3 | Q 5 | Page 130

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The compound interest on Rs $10000$ in $2$ years at $4%$ per annum being compounded half yearly is A. $Rs\text{ 832}\text{.24}$B. $Rs\text{ 828}\text{.82}$C. $Rs\text{ 824}\text{.32}$D. $Rs\text{ 912}\text{.86}$

Answer

Verified

Hint: First we recall the definition and formula of compound interest and then calculate the compound interest. The formula used to calculate the compound interest is
Compound interest = Amount – Principal
And \[\text{Amount =}P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]
Where, $P=$ Principal
\[R=\] Rate of interest
$T=$Time period

Complete step by step answer:
Now, we have given that Principal sum $=10,000$
Rate of interest $=4%$ per annum
Time period \[=2\text{ years}\]
We have given that the compound interest being compounded half yearly, so the time period will be $4\text{ years}$and the rate of interest will be half i.e. $2%$ because when interest is compounded half yearly the rate of interest will be $\dfrac{R}{2}$.
Now, we have to calculate the Amount, so we put all values in the formula
\[\text{Amount =}P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]
$\Rightarrow 10000{{\left( 1+\dfrac{2}{100} \right)}^{4}}$
$\begin{align}
  & \Rightarrow 10000{{\left( 1+\dfrac{1}{50} \right)}^{4}} \\
 & \Rightarrow 10000\times \left( \dfrac{51}{50} \right)\times \left( \dfrac{51}{50} \right)\times \left( \dfrac{51}{50} \right)\times \left( \dfrac{51}{50} \right) \\
 & \Rightarrow 10.2\times 10.2\times 10.2\times 10.2 \\
 & \Rightarrow 10824.32 \\
\end{align}$
The Amount will be Rs. $10824.32$
Now we have to calculate compound interest.
We know that Compound interest = Amount – Principal
Putting the values, Compound interest will be
 $\begin{align}
  & =10824.32-10000 \\
 & =824.32 \\
\end{align}$
So, the compound interest on Rs $10000$ in $2$ years at $4%$ per annum being compounded half yearly is $Rs.824.32$.

So, the correct answer is “Option C”.

Note: Compound interest is interest on interest; it means compound interest is additional amount of interest to the principal sum. Before calculating compound interest students have to calculate the amount by using the formula and then subtract principal from amount. Students must read questions carefully about the compounding frequency i.e. interest compounded yearly, half-yearly, quarterly, monthly or weekly. The time period will be changed accordingly.

Solution:

Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10% = 5% (compounded half yearly)

Time(n) = 1\ \frac{1}{2} years = 3 years (compounded half yearly)

Amount (A) = P\left(1+\frac{R}{100}\right)^n

= 10000\left(1+\frac{5}{100}\right)^3

= 10000\left(1+\frac{1}{20}\right)^3

= 10000\left(\frac{21}{20}\right)^3

= 10000\times\frac{21}{20}\times\frac{21}{20}\times\frac{21}{20}

= Rs. 11,576.25

Compound Interest (C.I.) = A – P

= Rs. 11,576.25 – Rs. 10,000 = Rs. 1,576.25

If it is compounded annually, then

Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10%, Time (n) = 1\ \frac{1}{2} years.

Amount (A) for 1 year = P\left(1+\frac{R}{100}\right)^n

= 10000\left(1+\frac{10}{100}\right)^1

= 10000\left(1+\frac{1}{10}\right)^1

= 10000\left(\frac{11}{10}\right)^1

= 10000\times\frac{11}{10}

= Rs. 11,000

Interest for \frac{1}{2} year = \frac{11000\times1\times10}{2\times100}=RS.\ 550

\therefore Total amount = Rs. 11,000 + Rs. 550 = Rs. 11,550

Now, C.I. = A – P = Rs. 11,550 – Rs. 10,000

= Rs. 1,550

Yes, interest Rs. 1,576.25 is more than Rs. 1,550.

What is the compound interest on 10000 for 2 years at 10% per annum?

What would be the compound interest on a principal of Rs 10000 Interest rate 10% for 3 years assuming interest is compounded semi annually?

What is the difference between the compound interest on 10000 for 2 years at 4% per annum compounded yearly and half yearly?

What is the compound interest on a sum Rs 10000 at 12% per annum for 1 year and 4 months when the interest is compounded at every 8 months?