What is the amount for Rs 10000 by compound interest?

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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An amount of Rs. 10,000 is compounded yearly at a 5% rate of interest for 2 years. If a certain amount is kept at a 10% rate of simple interest for 2 years then the interest earned is Rs. 350 less than that earned from the compound interest mentioned earlier. Calculate the value kept under simple interest.

1. Rs. 3375
2. Rs. 4225
3. Rs. 5750
4. Rs. 4750

Answer (Detailed Solution Below)

Option 1 : Rs. 3375

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Given:

Compound interest: P = 10000, R = 5%, n = 2

Simple Interest: R = 10%, n = 2

Formula used:

Simple interest: (P × R × T) / 100

Compound interest: Amount = P (1 + (R/100))n

Where, n = Number of years, P = Principal Amount, R = Rate of Interest, A = Amount

Calculations:

Find interest from amount compounded

⇒ A = 10000 × (1 + (5 / 100)2

⇒ A = 10000 × (1 + (1 / 20))2

⇒ A = 10000 × 21 × 21 / 400

⇒ A = 25 × 212

⇒ A = 11,025

⇒ I = 11025 – 10,000

⇒ I = 1025

Now, interest earned by simple interest

⇒ I = 1025 – 350

⇒ I = 675

⇒ 675 = P × 10 × 2 / 100

⇒ 67500 / 20 = P

⇒ P = 3375

∴ Value kept under simple interest is Rs. 3375

Last updated on Nov 4, 2022

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