Class 8 Maths Comparing Quantities Compound Interest

Compound Interest

Simple interest is calculated on the principal, or original, amount of a loan.

Let Principle = P, Rate = R% per annum, Time = n years.

Now, Simple Interest (SI) = (P * R * n)/100

Compound interest is calculated on the principal amount and also on the accumulated interest of

previous periods, and can thus be regarded as “interest on interest.”

1. When interest is compounded annually

Amount = P(1 + R/100)n

1. When interest is compounded Half-yearly

Amount = P{1 + (R/2)/100}2n

1. When interest is compounded annually but time is in fraction say 3

Amount = P(1 + R/100)3 * {1 + (2R/5)/100}

Now, Compound Interest (CI) = Amount - Principle (P)

Problem: Fabina borrows ₹ 12,500 per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?

Solution:

Here,

Principal (P) = ₹ 12,500, Time (T) = 3 years, Rate of interest (R) = 12% p.a.

Simple Interest for Fabina = (P * R * T)/100 = (12500 * 12 * 3)/100

= 125 * 12 * 13

= ₹ 4,500

Amount for Radha, P = ₹ 12,500, R = 10% and n = 3 years

Now, amount (A) = P(1 + R/100)n

= 12500(1 + 10/100)3

= 12500(1 + 1/10)3

= 12500(11/10)3

= 12500 * 11/10 * 11/10 * 11/10

= ₹ 16,637.50

So, C.I. for Radha = A – P = ₹ 16,637.50 – ₹ 12,500 = ₹ 4,137.50

Problem: Arif took a loan of ₹ 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1  years if the interest is:

(i) Compounded annually.                         (ii) Compounded half yearly

Solution:

(i) Here,

Principal (P) = ₹ 80,000, Time (n) = 1  years, Rate of interest (R) = 10%

Amount for 1 year (A) = P(1 + R/100)n

= 80000(1 + 10/100)1

= 80000(1 + 1/10)1

= 80000(11/10)1

= 80000 * 11/10

= ₹ 88,000

Interest for 1/2 year = (88000 * 10 *1)/(100 * 2) = ₹ 4,400

Total amount = ₹ 88,000 + ₹ 4,400 = ₹ 92,400

(ii) Here, Principal (P) = ₹ 80,000, Time (n) = 1  year = 3 half-years (compounded half yearly)

Rate of interest (R) = 10% = 5% (compounded half yearly)

Amount (A) = P(1 + R/100)n

= 80000(1 + 5/100)3

= 80000(1 + 1/20)3

= 80000(21/20)3

= 80000 * 21/20 * 21/20 * 21/20

= ₹ 92,610

Difference in amounts = ₹ 92,610 – ₹ 92,400 = ₹ 210

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