### Formulas, shortcuts, tricks and solved examples:

If P = Principal, A = Amount, R = Rate percent per year, T = T years, S.I = Simple interest, C.I = Compound interest, Then,
1. For Simple interest:
(A). S.I = (P × R × T)/100

(B) A = P + S.I
2. For Compound interest:
(A) When interest is compounded yearly,

(B) When interest is compounded half-yearly,

(C) When interest is compounded quarterly

(D) When time is in fraction of a year, say 2⅕

(E) If rate of interest in 1st year, 2nd year …………..… nth year are R1%, R2% …………. Rn% respectively, then,

3. Equivalent or Successive interest:
Single equivalent interest rate or Successive interest rate of 20% and 10% is

Single equivalent interest rate or Successive interest rate of 10%, 20% and 30% would be
Since, equivalent interest 10% and 20% is 28%
So, equivalent interest of 28% and 30% will be,

Example: 01
A sum of Rs. 15,500 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is Rs. 1060, the money lent at 8% is:
Solution:
Let the money lent at 8% be Rs. x, then
[(x × 8 × 1)/100] + [15500 - x) × 6 × 1/100] = 1060
or, 2x + 93000 = 106000
or, x = 6500
Therefore, the money lent at 8% is Rs. 6500
Example: 02
A sum of money at compound interest amounts to Rs. 10,580 in 2 years and to Rs. 12,176 in 3 years. The rate of interest per annum is:

Solution:
Interest on Rs. 10580 for 1 year = Rs. (12176 - 10580) = Rs. 1587
Rate = [(100 × 1587)/10580]% = 15%
Hence, the rate of interest per annum is 15%.
Example: 03
A sum of money becomes Rs. 13,380 after 3 years and Rs. 20,070 after 6 years on compound interest. The sum is:

Solution:
Let, the sum be x, then
x[1 + (R/100)]3 = 13380 and, x[1 + (R/100)]6 = 20070
On dividing, we get, [1 + (R/100)]3 = (20070/13380) = 3/2
x (3/2) = 13380
or, x = 13380 × (3/2) = 8920
Hence, the sum is Rs. 8920.

SOLVE EXAMPLE
Question No. 01
A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum?
(A) Rs. 4462.50
(B) Rs. 8032.50
(C) Rs. 8900
(D) Rs. 8925
Explanation:
Principal = Rs. (100 × 4016.25)/(9 × 5)
= Rs. (401625/45) = Rs. 8925.

Question No. 02
Calculate the amount on Rs. 4480 at 8% per annum for 3 years.
(A) Rs. 5555.20
(B) Rs. 5545.20
(C) Rs. 5000
(D) Rs. 6555
Explanation:
S.I. = (P × N × R)/100
= Rs. (4480 × 3 × 8)/100
= Rs. 1075.20
Amount = Rs. (4480 + 1075.20)
= Rs. 5555.20

Question No. 03
A certain sum of money at simple interest amounts to Rs. 1260 in 2 years and to Rs. 1350 in 5 years. The rate percent per annum is?
(A) 35 %
(B) 25 %
(C) 50 %
(D) 45 %
Explanation:
S.I. for 3 years = Rs. (1350 - 1260) = Rs. 90
S.I. for 2 years = Rs. (90/3) × 2 = Rs. 60
Principal = Rs. (1260 - 60) = Rs. 1200
Rate, R = (100 × 60)/(1200 × 2) % = 25 %

Question No. 04
Mr. Roy invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
(A) Rs. 6400
(B) Rs. 6500
(C) Rs. 7200
(D) Rs. 7500
Explanation:
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).
Then, [x × 14 × 2)/100] + [{(13900 - x) × 11 × 2}/100] = 3508
=> 28x - 22x = 350800 - (13900 × 22)
=> 6x = 45000
=> x = 7500.
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.

Question No. 05
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 3.5 years
(B) 4 years
(C) 4.5 years
(D) 5 years
Explanation:
Time = [(100 × 81)/( 450 × 4.5)] years = 4 years.

Question No. 06
A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
(A) 3.6%
(B) 4.5%
(C) 5%
(D) None of these
Explanation:
Let the original rate be R%. Then, new rate = (2R)%.
Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. for 1/3 year.
[(725 × R × 1)/100] + [362.50 × 2R × 1)/(100 × 3)] = 33.50
=> (2175 + 725) R = 33.50 × 100 × 3
=> (2175 + 725) R = 10050
=> (2900) R = 10050
=> R = (10050/2900) = 3.46
Original rate = 3.46%

Question No. 07
A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
(A) Rs. 35
(B) Rs. 245
(C) Rs. 350
(D) Cannot be determined
Explanation:
We need to know the S.I., principal and time to find the rate.
Since the principal is not given, so data is inadequate.

Question No. 08
Ravi took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 6
(C) 18
(D) None of these
Explanation:
Let rate = R% and time = R years.
Then, (1200 × R × R)/100 = 432
=> 12R2 = 432
=> R2 = 36
=> R = 6.

Question No. 09
S.I. on Rs. 1500 at 7% per annum for a certain time is Rs. 210. Find the time;
(A) 3 years
(B) 5 years
(C) 2 years
(D) 1½ years
Explanation:
Time, N = (210 × 100)/(1500 × 7) = 2 years

Question No. 10
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) Rs. 650
(B) Rs. 690
(C) Rs. 698
(D) Rs. 700