What is the compound interest on 10000 in 2 years at 4% per annum if the interest is compounded semi annually?

What is the compound interest on a sum Rs. 10,000 at 12% per annum for 1 year and 4 months, when the interest is compounded at every 8 months?

1. Rs. 1,364
2. Rs. 1,664
3. Rs. 1,504
4. Rs. 1,264

Answer (Detailed Solution Below)

Option 2 : Rs. 1,664

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SSC GD Previous Paper 2 (Held On: 13 Feb 2019 Shift 1)_Hindi

100 Questions 100 Marks 90 Mins

Given:

Principal = Rs. 10,000

Rate of interest = 12%

Time = 1 year and 4 months = 16 months

Formula used:

A = P (1 + r/100)n

C.I = A - P

Where, A = Amount, P = Principal, n = Time, C.I = Compound interest

Calculation:

Interest is compounded on 8 months,

So, Time = 16/8 = 2 years

Rate of interest = 12% × (8/12)  = 8%

A = P (1 + r/100)n

⇒ Amount = 10,000 × (1 + 8/100)2

⇒ Amount = 10,000 × (108/100)2

⇒ Amount = (108)2

⇒ Amount = Rs. 11,664

C.I = A - P

⇒ C.I = 11,664 – 10,000

⇒ C.I = 1,664

∴ The compound interest is Rs. 1,664.

Alternate Method

Interest is compounded on every 8 months

So, Time = 16/8 = 2 years

Rate of interest = 12% × (8/12)  = 8% 

Effective rate formula for two years = (A + B + AB/100)

Here, A = B = 8%

⇒ Effective rate formula for two years = {8 + 8 + (64/100)} = 16.64%

⇒ Compound interest = 10,000 × 16.64%

⇒ Compound interest = Rs. 1664

∴ The compound interest is Rs. 1,664.

Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!

Find the compound interest on Rs. 10000 in 2 year at 4% per annum, the interest being compounded half yearly?

1. Rs. 625.86
2. Rs. 827.54
3. Rs. 824.32
4. Rs. 896.56
5. Rs. 627.24

Answer (Detailed Solution Below)

Option 3 : Rs. 824.32

Free

SBI Clerk Prelims Full Test 1

100 Questions 100 Marks 60 Mins

Given:

P = Rs.10,000

Time = 4 years

Concept:

The interest is being compounded half yearly means it is being compounded twice every year.

In 2 years interest would be compounded 4 times.

Since the interest is calculated half yearly so the rate of interest will be half i.e. 2%.

As 4% rate is for whole year, so for half year it would be reduced to 2%

Calculation:

Using the formula for compound interest is,

\(\begin{array}{l} \Rightarrow {\rm{Amount}} = {\rm{P}}{\left( {1 + \frac{{\rm{R}}}{{100}}} \right)^{\rm{n}}}\\ \Rightarrow {\rm{Amount}} = 10000{\left( {1 + \frac{2}{{100}}} \right)^4}\\ \Rightarrow {\rm{Amount}} = 10000{\left( {\frac{{100 + 2}}{{100}}} \right)^4}\\ \Rightarrow {\rm{Amount}} = 10000{\left( {\frac{{102}}{{100}}} \right)^4}\\ \Rightarrow {\rm{Amount}} = 10000{\left( {\frac{{51}}{{50}}} \right)^4}\\ \Rightarrow {\rm{Amount}} = 10000 \times \frac{{51}}{{50}} \times \frac{{51}}{{50}} \times \frac{{51}}{{50}} \end{array}\)

⇒ Amount = 10824.32

Compound interest = Amount - principal

⇒ Compound interest = 10824.32 - 10000

∴ Compound interest = Rs. 824.32

Last updated on Sep 28, 2022

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