Question

Compound Interest compounded quarterly on Rs. 15000 for 3 years is Rs. 986 more than

Simple Interest on the same principal for 3 years. Find the rate of interest.​

Answer 1

Step-by-step explanation:

Quarterly interest paying for 3 years means 4 * 3 = 12 interest paying terms.

Let the rate of interest per year = r %

So, quarterly interest = (r/100) * (3/12) = r/400

Simple interest for 3 years = 15000 * (r/400) * 12 = 450r

Compound interest for 3 years

= 15000 * (1 + r/400)^12 - 15000

Since, compound interest = simple interest + 986

So, 15000 * (1 + r/400)^12 - 15000 = 450r + 986

Rearranging, 15000 * (1 + r/400)^12 - 450r = 986 + 15000 = 15986

Or, dividing both sides by 15000, we get,

(1 + r/400)^12 = 450r/15000 + 15986/15000

Or, (1 + r/400)^12 = 0.03r + 1.0657

Or (1 + r/400)^12 - 0.03r = 1.0657

This is an equation, that requires trial & error method to solve.

Assume r = 5%, LHS = (1 + 5/400)^12 - 0.03 * 5

= 1.011

Next assume r = 10% LHS = (1 + 10/400)^12 - 0.03 * 10 = 1.0449

Next assume r = 12%, LHS = (1 + 12/400)^12 - 0.03 * 12 = 1.0657

So, rate of interest = 12 % Ans.

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Answer 2

Step-by-step explanation:

Quarterly interest paying for 3 years means 4 * 3 = 12 interest paying terms.

Let the rate of interest per year = r %

So, quarterly interest = (r/100) * (3/12) = r/400

Simple interest for 3 years = 15000 * (r/400) * 12 = 450r

Compound interest for 3 years

= 15000 * (1 + r/400)^12 - 15000

Since, compound interest = simple interest + 986

So, 15000 * (1 + r/400)^12 - 15000 = 450r + 986

Rearranging, 15000 * (1 + r/400)^12 - 450r = 986 + 15000 = 15986

Or, dividing both sides by 15000, we get,

(1 + r/400)^12 = 450r/15000 + 15986/15000

Or, (1 + r/400)^12 = 0.03r + 1.0657

Or (1 + r/400)^12 - 0.03r = 1.0657

This is an equation, that requires trial & error method to solve.

Assume r = 5%, LHS = (1 + 5/400)^12 - 0.03 * 5

= 1.011

Next assume r = 10% LHS = (1 + 10/400)^12 - 0.03 * 10 = 1.0449

Next assume r = 12%, LHS = (1 + 12/400)^12 - 0.03 * 12 = 1.0657

So, rate of interest = 12 % Ans.