Question

what is the compound interest on rupees 200 for one year 10% rate compounded half yearly

1.rs 200
2.rs220.50
3.rs320.50
4.rs100.50​

Answer 1

Answer:

If the borrower and the lender agree to fix up an interval of time (say, a year or a half year or a quarter of a year etc) so that the amount (Principal + interest) at the end of an interval becomes the principal for the next interval, then the total interest over all the intervals, calculated in this way is called the compound interest and is abbreviated as C.I.

Compound interest at the end of a certain specified period is equal to the difference between the amount at the end of the period and original principal i.e. C.I. = Amount – Principal. In this section, we shall discuss some examples to explain the meaning and the computation of compound interest. Compound interest when interest is compounded annually.

Answer 2

Solution:

It is given that:

Principal amount = Rs.200

Rate of interest = 10%

Time period = 1 year

Mode of compounding = Half-yearly

The formula to be used is that of being compound half-yearly which is as follows:

$\sf{\implies\:Amount=P\left(1+\dfrac{R}{200}\right)^{2n}}$

Substituting the values in the equation:

$\sf{\longrightarrow\:Amount=200\left(1+\dfrac{10}{200}\right)^{2\times1}}$

$\sf{\longrightarrow\:Amount=200\left(1+\dfrac{1}{20}\right)^2}$

$\sf{\longrightarrow\:Amount=200\times\dfrac{21}{20}\times\dfrac{21}{20}}$

$\sf{\longrightarrow\:Amount=\dfrac{21}{2}\times\dfrac{21}{2}}$

$\sf{\longrightarrow\:Amount=\dfrac{21\times21}{2}}$

$\sf{\longrightarrow\:Amount=\dfrac{441}{2}}$

$\sf{\longrightarrow\:Amount=220.50}$

Hence the amount is:

2️⃣ Rs.220.50

Now, the next formula to find the compound interest is:

$\sf{\implies\:C.I=Amount-Principal}$

Here:

Amount = Rs.220.50

Principal amount = 200

$\sf{\longrightarrow\:C.I=220.50-200}$

$\sf{\longrightarrow\:C.I=20.50}$

The compound interest is Rs.20.50.

⇒ Final answers:

✳ Amount = Rs.220.50

✳ C.I = Rs.20.50