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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]

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.
2.	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.
3.	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.
4.	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.

6.	In how many years will a sum of money double itself at 10% per annum?
	A. 2 years 4 months B. 4 years 2 months C. 8 years 4 months D. 10 years 8 months

Ans: C.

Sol.
Let sum = x. Then, S.I. = x
∴ Time = [100 * S.I. / P*R] = [100 * x / x * 12] years
= 8 1/3 years = 8 years 4 months.

7.	A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
	A. 500 B. 698 C. 780 D. 910

Ans: B.

Sol.
S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs. (39 * 3) = Rs. 117.
∴ Principal = Rs. (815 - 117) = Rs. 698.

8.	The simple interest on Rs. 10 for 4 months at the rate of 3 paise per rupeeper month is :
	A. 1.20 B. 1.40 C. 2.25 D. 3.21

Ans: A.

Sol.
S.I. = Rs. [10 * 3/100 * 4] = Rs. 1.20

9.	The simple interest at x% for x years will be Rs. x on sum of:
	A. x B. 100x C. [100/x] D. [x/100]

Ans: C.

Sol.
Sum = [100 * S.I. / R * T] = Rs. [100 * x / x * x] = Rs. [100/x].

10.	A sum fetched a otal simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
	A. 8925 B. 8259 C. 8529 D. 8952

Ans: A.

Sol.
Principal = Rs. [100 * 4016.25 / 9 * 5] = Rs. [401625 / 45] = Rs. 8925.