Which will earn more interest and how much? ₹ 6000 lent at 12 % p.a. compounded annually for 1 1 2 years. ₹ 6000 lent at 12 % p.a. compounded half yearly for 1 1 2 years.

It is given that the principal P = ₹ 6000 , Rate of interest R = 12 % , Time n = 1 1 2 years For the interest compounded yearly, the time is in fraction, so A = P 1 + R 100 1 + 1 2 × R 100 ⇒ A = 6000 1 + 12 100 1 + 1 2 × 12 100 ⇒ A = 6000 × 112 100 × 106 100 ⇒ A = 71232000 10000 ⇒ A = ₹ 7123 . 2 we know that, Compound interest C I = A - P ⇒ C I = ₹ 7123 . 2 - ₹ 6000 ⇒ C I = ₹ 1123 . 2 Therefore, compound interest compounded yearly is ₹ 1123 . 2 . For the interest compounded half yearly the rate becomes half and the time becomes twice (as there are two half years in a year). So, here, Principal P = ₹ 6000 , Rate of interest R = 12 % per annum = 12 2 % half years = 6 % half year. Time n = 1 1 2 years = 3 2 years = 3 2 × 2 half years = 3 half years. We know that, A = P 1 + R 100 n ⇒ A = 6000 × 1 + 6 100 3 ⇒ A = 6000 × 106 100 × 106 100 × 106 100 ⇒ A = 7146096000 1000000 ⇒ A = ₹ 7146 . 096 Also, compound interest C I = A - P ⇒ C I = ₹ 7146 . 096 - ₹ 6000 ⇒ C I = ₹ 1146 . 096 Therefore, the compound interest compounded half yearly is ₹ 1146 . 096 Hence, the difference between the compound interest is: = ₹ 1146 . 096 - ₹ 1123 . 2 = ₹ 22 . 896 Clearly, we can observe that the ₹ 6000 lent at 12 % p.a. compounded half yearly for 1 1 2 years will earn ₹ 22 . 896 more as interest.

E M B I B E

Number Magic a textbook of Mathematics 8>Chapter 15 - Comparing Quantities III Compound Interest>EXERCISE>Q 9

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IMPORTANT

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Anita borrowed $₹ 50000$ for $1$ year $5$ months at $12 %$ per annum compounded annually. How much money will she have to pay back to settle the account.

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Important Questions on Comparing Quantities III Compound Interest

MEDIUM

8th CBSE

IMPORTANT

Number Magic a textbook of Mathematics 8>Chapter 15 - Comparing Quantities III Compound Interest>EXERCISE>Q 10

How much will

₹ 25000

amount to in

2

years at compound interest compounded annually, if the rates for successive years be

4 %

p.a. and

5 %

p.a.

MEDIUM

8th CBSE

IMPORTANT

Number Magic a textbook of Mathematics 8>Chapter 15 - Comparing Quantities III Compound Interest>EXERCISE>Q 11

A man borrows

₹ 1000

at

10 %

p.a simple interest for

3

years. He immediately lends this money out at compound interest at the same rate for the same time. What is his gain at the end of

3

years.

MEDIUM

8th CBSE

IMPORTANT

Number Magic a textbook of Mathematics 8>Chapter 15 - Comparing Quantities III Compound Interest>EXERCISE>Q 12

Which will earn more interest and how much?

$₹ 6000$ lent at $12 %$ p.a. compounded annually for $1 \frac{1}{2}$ years.
$₹ 6000$ lent at $12 %$ p.a. compounded half yearly for $1 \frac{1}{2}$ years.