Question

Vasudevan invested ₹ 60000 at an interest rate of 12% per annum compounded half yearly. What amount would he get
(i) after 6 months?
(ii) after 1
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Answer 1

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Solution:

Given that, Vasudevan invested ₹ 60,000

For Compound Interest (C.I.)

A = P[1 + (r/100)]^n

P = ₹ 60,000

n = 6 months and 1 year

R = 12% p.a. compounded half-yearly

where , A = Amount, P = Principal, n = Time period and R = Rate percent

(i) For easy calculation of compound interest, we will put Interest Rate as 6% half-yearly and n = 1.

Compound Interest to be paid for 6 months

A = P[1 + (r/100)]^n

A = 60000[1 + (6/100)]^1

A = 60000[(100/100) + (6/100)]

A = 60000 × (106/100)

A = 60000 × 1.06

A = ₹ 63600

(ii) Compound Interest to be paid for 12 months (1 year) compounded half yearly.

So, assume n = 2, r = 6%

A = P[1 + (r/100)]^n

A = 60000[1 + (6/100)]^2

A = 60000[(100/100) + (6/100)]^2

A = 60000 × (106/100) × (106/100)

A = 60000 × (11236/10000)

A = 60000 × 1.1236

A = ₹ 67416

Answer 2

Answer:

Qu€stion:-

Vasudevan invested ₹ 60000 at an interest rate of 12% per annum compounded half yearly. What amount would he get

(i) after 6 months?

(ii) after 1

Answers :-

$\boxed{\underline{\tt \red{(i) ₹63,600}}}$

$\boxed{\underline{\tt \red{(ii) ₹67,416}}}$

$\huge \rm \green{\underline{Explanation✧}}$

(i)

P = ₹ 60,000

R = 12%

T = 6 months = 1/2 year

COMPOUNDED HALF YEARLY

P = ₹ 60,000

R = 12% = (12/2)% =6%

T = 1/2 = (1/2)×2 = 1 year

A = P( 1 + R/100)^n

= ₹ 60,000( 1 + 6/100)¹

= ₹ 60,000 ( 1 + 3/50)¹

= ₹ 60,000 (53/50)¹

= ₹ 60,000 × 53/50

= ₹ 63,600

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(ii)

P = ₹ 60,000

R = 12%

T = 1 year

COMPOUNDED HALF YEARLY

P = ₹ 60,000

R = 12% = (12/2)% =6%

T = 1 = 1×2 = 2 year

A = P( 1 + R/100)^n

= ₹ 60,000( 1 + 6/100)²

= ₹ 60,000 ( 1 + 3/50)²

= ₹ 60,000 (53/50)²

= ₹ 60,000 × 53/50 × 53/50

= ₹ 67,416

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