Simple Interest and Compound Interest Tricks

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

Simple Interest

Formula of Simple Interest:

Simple Interest and Compound Interest Tricks PDF

Examples

#1

Find the simple interest, If

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

# Solution

4×20×10 ⇒ 800
2×5 = 10
6×2×3×2 = 72
5×2×5=50
4×2=8
73/3=24
37.50

#2

Find the following:

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

# Solution:

S.I = 6 ; A = S.I + principal ; A = 6 + 100 ⇒ 106
S.I = 10 ; A = S.I + P ; A = 10+500 ⇒ 510
S.I = 6 ; A = 400 + 6 ⇒ 406
T = 5 yr.
120

#3

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 %.
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)
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)
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?
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.

Practice Set for Simple Interest

# Solution

Principal = 600, R = 10%
12000
112.50
[ 1164-1008 = 156 ] ⇒ ¹⁵⁶/_3×4 = 208 ; R = ²⁰⁸/_2×800×100 ⇒ 13
^7x/₂₀ - ^3x/₁₀ = 40 ⇒ x = ( 40 × 20 ) ⇒ x = 800 [ Hint : Given Below ]

Compound Interest

Formula of Compound Interest:

Trick :

Calculating Compound Interest for 3 Years

Calculating Compound Interest for 4 year

# 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 .

Practice Set for Compound Interest