Question

find the compound interest on rs 10000 for 12 months at 10% per annum, if the intrest is compounded a) annually b) halfyearly
plss answer ​

Answer 1

Given:-

• Principal = ₹10000
• Time = 12 months = 1 year
• Rate = 10% p.a.

To Find:-

Compound interest if the interest is compounded:-

• a) annually
• b) half yearly

Solution:-

a) Compounded annually

→ We know,

• A = P(1 + r/100)ⁿ

Hence,

Let us calculate the amount first.

= A = 10000(1 + 10/100)¹

⇒ A = 10000(1 + 1/10)¹

⇒ A = 10000(11/10)¹

⇒ A = 10000 × 11/10

⇒ A = 11000

∴ Amount of the interest is compounded annually is ₹11000

Now,

Let us calculate CI

We know,

• CI = Amount - Principal

Hence,

CI = 11000 - 10000

⇒ CI = ₹1000

∴ CI after 1 year if the interest is compounded annually will be ₹1000.

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b) Compounded half-yearly

→ We know,

• A = P(1 + r/200)²ⁿ

Hence,

= A = 10000(1 + 10/200)²*¹

⇒ A = 10000(1 + 1/20)²

⇒ A = 10000(21/20)²

⇒ A = 10000 × 21/20 × 21/20

⇒ A = 11025

∴ Amount if the interest is compounded half-yearly is ₹11025.

Now,

Let us calculate the CI

CI = 11025 - 10000

⇒CI = 1025

∴ The compound interest is the interest is compounded half-yearly will be ₹1025.

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Answer 2

Answer:

Given

Principal - rs 10000

Time - 12 month's

Rate - 10%

To find

a) annually

b) half-yearly

We know that:-

Amount = P(1 + $\frac{R}{100}$ )t

We have interest compounded half-yearly

thus, Time = 2 × (year's) = 2 rate

= $\frac{R}{2} = \frac{10}{2}$= 5 it means 5% interest after every six months

Formula to find interest:-

interest will be A = P(1 + $\frac{ \frac{R}{2} }{100})$t×2

According to Question:-

Amount = p$(1 + \frac{r}{100}$)t

$\frac{R}{2} = \frac{10}{2}$= 5 and time = $\frac{12months}{6months}$ = 2

it means that the men will get an interest of 5% after every 6 month's

Total amount, P(1 + $\frac{R}{100}$ )t

$10000 \times (1 + \frac{5}{100)}$)²

$10000 \times (\frac{105}{100}$)²

= $\frac{10000 \times 105 \times 105}{100 \times 100}$

= 105×105

=11025

The total amount = Rs.$\boxed{\red{11025}}$

★Now, Compound interest = (total amount) - (principal amount)

• total amount - Rs.11025
• Principal amount - Rs.10000

Rs. 11025 - 10000

= Rs.1025

The Compound interest = $\boxed{\red{Rs.1025}}$