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## SIMPLE INTEREST -> IMPORTANT FORMULAE

 1. Principal : The money borrowed or lent out for a certain priod is called the principal of he sum. 2. Interest : Extra money paid for using other’s money is called interest. 3. Simple Interest (S.I.) : If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called simple interest. Let Principal = P, Rate = R% per annum (p.a.) and Time = T years, Then, (i) S.I. = [P * R * T / 100] (ii) P = [100 * S.I. / R * T] R = [100 * S.I / P * T] and T = [100 * S.I. / P * R]

## SIMPLE INTEREST -> SOLVED EXAMPLES

1. At what rate percent per annum will a sum of money double in 16 years? Sol. Let principal = P. Then, S.I. = P and T = 16 years ∴ Rate = [100 * P / P * 16]% = 6 1/4% p.a. The simple interest on a sum of money is 4/9 of the principal. Find the rate percent and time, if both are numerically equal. Sol. Let sum = Rs. x Then, S.I. = Rs. 4x/9 Let rate = R% and time = R years. Then, [x * R * R / 100] = 4x / 9 or R² = 400/9 or R = 20/3 = 6 2/3 ∴ Rate = 6 2/3 % and Time = 6 2/3 yrs = 6 yrs 8 months. A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2% higher rate, it would have fetched Rs. 360 more. Find the sum. Sol. Let sum = P and original rate = R. Then, [P * (R+2) * 3 / 100] - [P * R * 3 / 100] = 360 ⇔ 7x/20 - 3x/10 = 40 ⇔ x = (40 * 20) = 800. Hence, the sum is Rs. 800. Find the simple interest on Rs. 68,000 at 16 2/3 % per annum for 9 months. Sol. Let sum = P and original rate = R. Then, [P * (R+2) * 3 / 100] - [P * R * 3 / 100] = 360 ⇔ 7x/20 - 3x/10 = 40 ⇔ x = (40 * 20) = 800. Hence, the sum is Rs. 800.

## SIMPLE INTEREST -> EXERCISE

1. Simple interest on a certain sum at a certain annual rate of interest is 1/9 of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is:

• A. 5
• B. 8
• C. 3 1/3
• D. 2 2/3
 Ans: C. Sol. Let sum = x. Then, S.I. = x/9 Let rate = R% and time = R years. ∴ [x * R * R / 100] = x / 9 ↔ R’ = 100/9 ⇔ R = 10/3 = 3 1/3. Hence, time = 3 1/3 %.

2. Simple interest on a certain amount is 9/16 of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is :

• A. 6 1/2
• B. 7 1/2
• C. 8
• D. 9 1/2
 Ans: B. Sol. Let sum = x. Then, S.I. = 9/16 x. Let rate = R% and time = R years. ∴ [x * R * R / 100] = 9x / 16 ⇔ R² = 900/16 ⇔ R = 30/4 = 7 1/2 Hence, time = 7 1/2 years.

3. How long will it take a sum of money invested at 5% p.a. S.I. to increase its value by 40%?

• A. 6 years
• B. 7 years
• C. 8 years
• D. 9 years
 Ans: C. Sol. Let the sum be x. Then, S.I. = 40% of x = 2x/5; Rate = 5%. ∴ Time = [100 * 2x/5 * 1/x*5] = 8 years.

4. At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years?

• A. 4 %
• B. 5 %
• C. 6 %
• D. 7 %
 Ans: A. Sol. Let sum = x. Then, S.I. = 2x/5, Time = 10 years. ∴ Rate = [100 * 2x / x*5*10]% = 4%.

5. The rate at which a sum becomes four times of itself in 15 years at S.I., will be :

• A. 10 %
• B. 15 %
• C. 20 %
• D. 40 %
 Ans: C. Sol. Let sum = x. Then, S.I. = 3x ∴ Rate = [100 * S.I. / P*T] = [100 * 3x / x * 15]% = 20%.