Question

compute the compound interest on rs.3200 for 1 year at 8 % per annum when compounded halfyearly??​

Answer 1

Answer :

• The Compound Interest in Rs. 3200 for 1 year at the rate of 8% p.a. (Compounded half-yearly) is 261.12 .

Explanation :

Given :

• Principal of the transaction, P = Rs. 3200

• Time period, n = 1 year

• Rate of interest, R% = 8% p.a.

To find :

• The Compound Interest in Rs. 3200 for 1 year at the rate of 8% p.a. (Compounded half-yearly) , CI = ?

Knowledge required :

Formula for Compound Interest (Compounded

half-yearly) :

⠀⠀⠀⠀⠀⠀⠀⠀⠀CI = P[(1 + R/200)^2n - 1]

Where :

• CI = Compound Interest
• R = Rate of interest
• n = Time period
• P = Principal

Solution :

By using the formula for Compound Interest (Compounded half-yearly) , we get :

==> CI = P[(1 + R/200)^2n - 1]

==> CI = 3200 × [(1 + 8/200)^(2 × 1) - 1]

==> CI = 3200 × [(208/200)² - 1]

==> CI = 3200 × (208/200 × 208/200 - 1)

==> CI = 3200 × (43264/40000 - 1)

==> CI = 3200 × [(43264 - 40000)/10000]

==> CI = 3200 × 3264/10000

==> CI = 10444800/40000

==> CI = 261.12

∴ CI = Rs. 262.12

Therefore,

• The Compound Interest is Rs. 261.12

Answer 2

$\large{\red{\bigstar}\pink{\boxed{\sf{Given}}}}$

▩Principal = Rs.3200

▩Rate = 8%

▩Time = 1year = 2half

$\large{\red{\bigstar}\pink{\boxed{\sf{Find}}}}$

▩Compound Interest

$\large{\red{\bigstar}\pink{\boxed{\sf{Solution}}}}$

we, know that

$\underline{\boxed{\sf A = P{\bigg\lgroup {\sf 1 + \dfrac{R}{100}}\bigg\rgroup }^T}}$

where,

• Principal, P = Rs.3200
• Rate, R = 8%
• Time, t = 2half years

So,

$\dashrightarrow\sf Amount = P{\bigg\lgroup {\sf 1 + \dfrac{R}{100}}\bigg\rgroup }^T$

$\dashrightarrow\sf Amount = 3200{\bigg\lgroup {\sf 1 + \dfrac{8}{100}}\bigg\rgroup }^2$

$\bigstar\sf Taking \: L.C.M$

$\dashrightarrow\sf Amount = 3200{\bigg\lgroup {\sf\dfrac{100 + 8}{100}}\bigg\rgroup }^2$

$\dashrightarrow\sf Amount = 3200{\bigg\lgroup {\sf\dfrac{108}{100}}\bigg\rgroup }^2$

$\dashrightarrow\sf Amount = 3200{\bigg\lgroup {\sf1.08}\bigg\rgroup }^2$

$\dashrightarrow\sf Amount = 3200 \times 1.08 \times 1.08$

$\dashrightarrow\sf Amount = 3200 \times 1.1664$

$\dashrightarrow\sf Amount =Rs. 3732.48$

$\small{\therefore\sf Amount =Rs. 3732.48}$

Now, we know

$\underline{\boxed{\sf Compound \: Interest = Amount - Principal}}$

where,

• Amount, A = Rs.3732.48
• Principal, P = Rs.3200

So,

$\implies\sf Compound \: Interest = Amount - Principal$

$\implies\sf Compound \: Interest = 3732.48- 3200$

$\implies\sf Compound \: Interest = Rs.532.48$

$\small{ \frak{\therefore Compound \: Interest = Rs.532.48}}$

Thus, Compund Interested is Rs.532.48