What is the amount for rupees 10000 by compound interest at 8% rate for 2 years?

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.

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.

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

Solution:

What is known: Principal, Time Period, and Rate of Interest

What is unknown: Amount and Compound Interest (C.I.)

Reasoning:

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

P = ₹ 10,000

n = \(1{\Large\frac{1}{2}}\) years

R = 10% p.a. compounded annually and half-yearly

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

For calculation of C.I. compounded half-yearly, we will take the Interest rate as 5% and n = 3

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

A = 10000[1 + (5/100)]3

A = 10000[1 + (1/20)]3

A = 10000 × (21/20)3

A = 10000 × (21/20) × (21/20) × (21/20)

A = 10000 × (9261/8000)

A = 5 × (9261/4)

A = 11576.25

Interest earned at 10% p.a. compounded half-yearly = A - P

= ₹ 11576.25 - ₹ 10000 = ₹ 1576.25

Now, let's find the interest when compounded annually at the same rate of interest.

Hence, for 1 year R = 10% and n = 1

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

A = 10000[1 + (10/100)]1

A = 10000[1 + (1/10)]

A = 10000 × (11/10)

A = 11000

Now, for the remaining 1/2 year P = 11000, R = 5%

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

A = 11000[1 + (5/100)]

A = 11000[(105/100)]

A = 11000 × 1.05

A = 11550

Thus, amount at the end of \(1{\Large\frac{1}{2}}\)when compounded annually = ₹ 11550

Thus, compound interest = ₹ 11550 - ₹ 10000 = ₹ 1550

Therefore, the interest will be less when compounded annually at the same rate.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 8

Video Solution:

Find the amount and the compound interest on ₹ 10,000 for \(1{\Large\frac{1}{2}}\) years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 8

Summary:

The amount and the compound interest on ₹ 10,000 for \(1{\Large\frac{1}{2}}\) years at 10% per annum, compounded half-yearly is  ₹ 11576.25 and  ₹ 1576.25 respectively. The interest will be less when compounded annually at the same rate.

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