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# Tips, Tricks And Shortcuts Of Compound Interest

## Tips, Tricks And Shortcuts Of Compound Interest

Compound interest is the interest calculated on the initial principal and also includes all the interest of previous periods on a deposit or loan

Compound Interest can be calculated , CI = P $(1+ \mathbf{\frac{r}{100}})^{n}$

Total Amount can be calculated, A = P $(1+ \mathbf{\frac{r}{100}})^{n}$

### Tips and Tricks and Shortcuts on Compound Interest

• Here, are quick and easy tips and tricks on Compound Interest. Learn the tricks and concept of compound interest.
• There are mainly 5 types of questions asked in exams. However, these questions can be twisted to check the students understanding level of the topic but it can be solved using tips and tricks.

### Compound Interest Tricks and Tips and Shortcuts

• A sum of money placed at compound interest becomes x time in ‘a’ years and y times in ‘b’ years. These two sums can be related by the following formula:
$\mathbf{x^{\frac{1}{a}}=y^{\frac{1}{b}}}$
• If an amount of money grows up to Rs x in t years and up to Rs y in (t+1) years on compound interest, then
r% = $\mathbf{\frac{y-x}{x}* 100}$
• A sum at a rate of interest compounded yearly becomes Rs. A1 in t years and Rs. A2 in (t + 1) years, then
P = A1($\mathbf{\frac{A_{1}}{A_{2}}}$)

### Type 1: Tips and Tricks to find the compound interest (Yearly, Quarterly, and Half-yearly)

Question 1. Find the amount if Rs 50000 is invested at 10% p.a. for 4 years

Options:

A. 73205

B. 7320.5

C. 73250

D. 73502

Solution:    We know that,

Amount = P $(1+ \frac{r}{100})^{n}$

A =50,000$(1+ \frac{10}{100})^{4}$

A = 50000 (1.1)4

A = 73205

Correct option: A

### Type 2: Tips and Tricks and Shortcuts for Compound Interest (To find the Rate of Interest, Time period, Principal)

Question 1. The Compound Interest on a sum of Rs 576 is Rs 100 in two years. Find the rate of interest.

Options:

A. 7.33%
B. 4.33%
C. 8.33%
D. 5.33%

Solution:     We know that,

Amount = Compound  Interest + Principal

A = 576 + 100 = 676

Amount =P $(1+ \frac{r}{100})^{n}$

676 =576 $(1+ \frac{r}{100})^{2}$

$\frac{676}{576}$=$(1+ \frac{r}{100})^{2}$

($\frac{26}{24}$)2 = $(1+ \frac{r}{100})^{2}$

$\frac{26}{24}$=$(1+ \frac{r}{100})$

($\frac{26}{24}$ – 1) =$\frac{r}{100}$

1.0833 – 1 =$\frac{r}{100}$

0.0833 = $\frac{r}{100}$

r = 8.33%

Correct option: C

### Type 3: Tips and Tricks to Find sum or rate of interest when compound interest and S.I are given

Question 1. The difference between the CI and SI on a certain amount at 14% p.a. for 2 years is Rs. 100. What will be the value of the amount at the end of three years if compounded annually?

Options:

A. 7558.89
B. 7500.45
C. 7558
D. 7554.56

Solution:    We know that, Difference between CI and SI for 2 years , Difference  = $\frac{P(R)^{2}}{(100)^{2}}$

100 = $\frac{P(14)^{2}}{(100)^{2}}$

P =$\frac{100(100)^{2}}{(14)^{2}}$

P =$\frac{1000000}{196}$

P = 5102.04

Now calculate the CI on Rs. 5102.04

A = 5102.04 $(1+ \frac{14}{100})^{3}$

A =5102.04 $( \frac{114}{100})^{3}$

A = 5102.04 * 1.48

A= 7558.89

Correct option: A

### Type 4: Shortcuts of Compound Interest (When sum of money becomes x time in ‘a’ years and y times in ‘b’ years.)

Question 1. A sum of money placed at compound interest doubles itself in 8 years. In how many years will it amount to 32 times itself?

Options:

A. 40 years
B. 50 years
C. 32 years
D. 35 years

Solution:     We know that,

$x^{\frac{1}{a}}$ = $y^{\frac{1}{b}}$

$2^{\frac{1}{8}}$ = $32^{\frac{1}{x}}$

$2^{\frac{1}{8}}$ = $2^{\frac{5}{x}}$

$\frac{1}{8}$ = $\frac{5}{x}$

x = 40 years

Correct option: A

### Type 5: Tips and Shortcuts for Compound Interest (When Rates are different for different years)

Question 1. Find the compound interest on a sum of money of Rs.10000 after 2 years, if the rate of interest is 2% for the first year and 4% for the next year?

Options:

A. Rs. 304
B. Rs. 608
C. Rs. 1000
D. Rs. 710

Solution:    We know that,

Amount = $P (1+\frac{r_{1}}{100}) (1+\frac{r_{2}}{100}) (1+\frac{r_{3}}{100})$

Here, r1 = 2% r2 = 4% and p = Rs.10000,

CI = A – P

CI = $10000 (1 + \frac{2}{100}) (1 + \frac{4}{100}) – 10000$

CI = $10000 * (\frac{102}{100})(\frac{104}{100}) – 10000$

CI = $10000 * (51 * \frac{52}{2500}) – 10000$

CI = $10000 * (\frac{2652}{2500}) – 10000$

CI = 10000 * (1.06) – 10000

CI = 10608 – 10000

CI = 608

Hence, the required compound interest is Rs. 608.

Correct option: B