What is the compound interest on Rupees 8000 at 10% per annum for 2 years if the interest is calculated half yearly?

Answer

Hint: making use of the formula of compound interest.
$p {\left( {1 + \dfrac{R}{{100}}} \right)^t}$. Where P is Principal, R is Rate, t is time.Complete step-by-step answer:

In the given question we are provided
Principle, P=8000
Rate, R=5%
Time, t=3
Making use of formula
$P {\left( {1 + \dfrac{R}{{100}}} \right)^t}$. Substitute the values in this formula, we get
$
  8000{\left( {1 + \dfrac{5}{{100}}} \right)^3} \\
   = 8000{\left( {\dfrac{{105}}{{100}}} \right)^3} \\
   = 8000 \times \dfrac{{105}}{{100}} \times \dfrac{{105}}{{100}} \times \dfrac{{105}}{{100}} \\
   = 9261 \\
 $
So compound interest is 9261.

Note: For per annum compound interest is calculated for the whole year. But if in a question it was asked for half-yearly too we have to take a time period of 6 months. The calculation should be done properly.

Compound interest is the total annual interest earned over a set period of time on a loaned principal.

The amount of money remaining at the end is called the amount.

The entire compound interest earned is the sum of the initial principal and the total compound interest earned.

It is given that

Principal (P) = ₹ 8000

Rate of interest (r) = 10% p.a.

Period (n) = 4 years

We know that

Amount = \mathrm{P}(1+\mathrm{r} / 100)^{\mathrm{n}}

Substituting the values

= 8000(1+10 / 100)^{4}

By further calculation

= 8000 × 11/10 × 11/10 × 11/10 × 11/10

= ₹ 11712.80

Here

CI = A – P

Substituting the values

= 11712.80 – 8000

= ₹ 3712.80

Find the amount and the compound interest on Rs 8000 for \[1\frac{1}{2}\] years at 10% per annum, compounded half-yearly.

Solution

Given: 
P = Rs 8, 000
R = 10 % p . a . 
n = 1 . 5 years
When compounded half - yearly, we have: 
\[A = P \left( 1 + \frac{R}{200} \right)^{2n} \]
\[ =\text{ Rs }8, 000 \left( 1 + \frac{10}{200} \right)^3 \]
\[ =\text{ Rs }8, 000 \left( 1 . 05 \right)^3 \]
 = Rs 9, 261
Also, 
CI = A - P
 = Rs 9, 261 - Rs 8, 000
 = Rs 1, 261

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Solution : Principal `=` Rs `8000`<br>Time `= 1(1/2)` yrs<br>`n = 3`<br>Rate `= 10%` p.a. `= 5%` half yearly<br>So , Amount `= P ( 1 + R/100 )^n`<br>`= 8000 × ( 105 / 100 )^3`<br>`= ( 8 × 105 × 105 × 105 ) / 1000`<br>`= 9261` .<br>So , Compound Interest `=` Rs `9261 -` Rs `8000 =` Rs `1261`.

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