Simple Interest and Compound Interest Tricks PDF

Today I am going to share Simple Interest and Compound Interest tricks and shortcuts.

Simple Interest 

Examples

#1

Find the simple interest, If

1. P = Rs.1000, R = 20% per annum, T = 4 years.
2. P = Rs.600, R = 5% per annum, T = 4 months.
3. P = Rs.200, R = 6% per six months, T = 3 years.
4. P = Rs.500, R = 2% per six months, T = ⁵/₂ years.
5. P = Rs.400, R = 3% per three months, T = 2 months.
6. P = Rs.730, R = 10% per annum, T = 120 days.
7. P = Rs. 3000, R = 61/4 per annum, T = period from 4th Feb to 18th Apr.

# Solution

#2 

Find the following:

1. P = Rs. 100, R = 3% per annum, T = 2 year, A= ?
2. P = Rs. 500, R = 6% per annum, T = 4 months, A= ?
3. P = Rs. 400, R = 3.65% per annum, T = 150 days, A= ?
4. A = Rs. 540, S.I = Rs. 108 , R = 5%, T = ?
5. A = Rs. 1,120, R = 5%, T = 2²/₅ yr, S.I = ?

# Solution:

1. S.I = 6 ; A = S.I + principal ; A = 6 + 100 ⇒ 106
   
2. S.I = 10 ; A = S.I + P ; A = 10+500 ⇒ 510
3. S.I = 6 ; A = 400 + 6 ⇒ 406
   
4. 
   
   
5. 

#3 

1. A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. Find the sum and the rate %.
2. Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of Rs. 11,400 at the end of nine years , how much money did he borrow ?(Bank P.O 1999)
3. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6¹/₄% p.a. for 2 years. Find his gain in the transaction per year.(S.S.C.2000)
4. A certain sum of money amounts to Rs. 1008 in 2 years and to Rs. 1164 in 3¹/2 years.Find the sum and the rate of interest?
5. The simple interest on a certain sum of money for 2¹/2 years at 12% per annum is Rs. 40 less than the simple interest on the same sum for 3¹/2 years at 10% per annum. Find the sum.

# Solution

1. Principal = 600, R = 10%
   
2. 
3. 
   
   
4. [ 1164-1008 = 156  ] ⇒ ¹⁵⁶/_3×4 = 208 ; R = ²⁰⁸/_2×800×100 ⇒ 13
5. ^7x/₂₀ - ^3x/₁₀ = 40 ⇒ x = ( 40 × 20 ) ⇒ x = 800 [ Hint : Given Below ]
   

# Compound Interest 

# Formulas 

Case 1. When interest is not Compound yearly,

Amount after 't' years A = P [1+ ^r/_n×100]^nt

n= no of compounding per year

When interest is compounded half yearly, n = 2

compounded quarterly, n = 4

compounded monthly, n = 12

Case 2. When rate % is no equal every year and interest is compounded yearly

 Basic formula :
P [1+ ^r/₁₀₀] [1+ ^r/₁₀₀] ...upto 't' times
But as rate % is not same every year, so
A = P [1+ ^r1/₁₀₀]^t1 [1+ ^r2/₁₀₀]^t2 .... and so on
Where R1 = Rate% p.a. for t1 years. and R2 = Rate % p.a. for t2 years.
Case 3 When interest is compounded yearly but time is in fraction
T = 5³/_{4 years}
A= (whole part) × (fraction part of time )
A = P [1+ ^r/₁₀₀]⁵ ×  [1+ ^3r/_4/100]

# Difference between Compound Interest and Simple Interest

CI - SI = P [ R/100 ]2

When time t = 3 years

CI - SI = P [ (^R/100³ +3 (^R/100)²]

# Examples

#1

• If the compound interest on a certain sum for two years at 10% p.a. is Rs 2,100 the simple interest on it at the same rate for two years will be. ( RRB, 2009)
• The compound interest on a sum for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound and simple interest for 3 years will be.
• The difference between simple interest and compound interest on a sum for 2 years at 8% when the interest is compounded annually is Rs. 16, if the interest were compounded half yearly, the difference in one interest would be nearly.
• The difference in C.I and S.I for 2 years on a sum of money is Rs. 160.If the S.I for 2 years be Rs. 2880, the rate of percent is .

# Solution

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