1 1/2 thecompound interest on rs 10000 at 12% per annum for years, compounded annually, is

Solution:

(a) Here, Principal (P) = Rs. 10800, Time (n) = 3 years Rate of interest (R) = 12\ \frac{1}{2}\%=\frac{25}{2\%}

Amount(A) = P\left(1+\frac{R}{100}\right)^n

= 10800\left(1+\frac{1}{8}\right)^3=10800\left(\frac{9}{8}\right)^3

= 10800\times\frac{9}{8}\times\frac{9}{8}\times\frac{9}{8}

= Rs. 15,377.34

Compound Interest (C.I.) = A – P

= Rs. 10800 – Rs. 15377.34 = Rs. 4,577.34

(b) Here, Principal (P) = Rs. 18,000, Time (n) = 2\ \frac{1}{2} years, Rate of interest (R) = 10% p.a.

Amount(A) = P\left(1+\frac{R}{100}\right)^n

= 18000\left(1+\frac{10}{100}\right)^2=18000\left(1+\frac{1}{10}\right)^2

= 18000\left(\frac{11}{10}\right)^2=18000\times\frac{11}{10}\times\frac{11}{10}

= Rs. 21,780

Interest for \frac{1}{2} years on Rs. 21,780 at rate of 10% = \frac{21780\times10\times1}{100}= Rs. 1089

Total amount for 2\ \frac{1}{2} years.

= Rs. 21,780 + Rs. 1089 = Rs. 22,869

Compound Interest (C.I.) = A – P

= Rs. 22869 – Rs. 18000 = Rs. 4,869

(c) Here, Principal (P) = Rs. 62500, Time (n) = 1\ \frac{1}{2}=\frac{3}{2} years = 3 years

Rate of interest (R) = 8% = 4% (compounded half yearly)

Amount (A) = P\left(1+\frac{R}{100}\right)^n

= 62500\left(1+\frac{4}{100}\right)^2

= 62500\left(1+\frac{1}{25}\right)^3

= 62500\left(\frac{26}{25}\right)^3

= 62500 \times\frac{26}{25}\times\frac{26}{25}\times\frac{26}{25}

= Rs. 70,304

Compound Interest (C.I.) = A – P

= Rs. 70304 – Rs. 62500 = Rs. 7,804

(d) Here, Principal (P) = Rs. 8000, Time (n) = 1 years = 2 years (compounded half yearly)

Rate of interest (R) = 9% = \frac{9}{2}\% (compounded half yearly)

Amount (A) = P\left(1+\frac{R}{100}\right)^n

= 8000\left(1+\frac{9}{2\times100}\right)^2

= 8000\left(1+\frac{9}{200}\right)^2

= 800\left(\frac{209}{200}\right)^2

= 8000\times\frac{209}{200}\times\frac{209}{200}

= Rs. 8,736.20

Compound Interest (C.I.) = A – P

= Rs. 8736.20 – Rs. 8000

= Rs. 736.20

(e) Here, Principal (P) = Rs. 10,000, Time (n) = 1 years = 2 years (compounded half yearly)

Rate of interest (R) = 8% = 4% (compounded half yearly)

Amount (A) = P\left(1+\frac{R}{100}\right)^n

= 10000\left(1+\frac{4}{100}\right)^2

= 10000\left(1+\frac{1}{25}\right)^2

= 10000\left(\frac{26}{25}\right)^2

= 10000\times\frac{26}{25}\times\frac{26}{25}

= Rs. 10,816

Compound Interest (C.I.) = A – P

= Rs. 10,816 – Rs. 10,000 = Rs. 816

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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