Tips Tricks And Shortcuts Of Compound Interest

Compound Interest Tips Tricks And Shortcuts

Compound interest is the interest calculated on the initial principal and also includes all the interest of previous periods on a deposit or loan. Here we can find Tips Tricks And Shortcuts Of Compound Interest.

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

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

Tips, Tricks And Shortcuts Of Compound Interest

Important Tips 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.

Important formulae on Compound Interest

  • 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: For different time period (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:  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:  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:  (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:  When C.I. 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