# Tips And Tricks And Shortcuts To Solve Compound Interest

### 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:
(x)1/a = (y)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% = (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(A1/A2)t ## 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+r/100)t
A = 50000 (1 + 10/100)4
A = 50000 (1.1)4
A = 73205

## 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+r/100)t
676 = 576 (1+ r/100)2
676/576 = (1+ r/100)2
(26/24)2 = (1+ r/100)2
(26/24) = (1+ r/100)
(26/24 – 1) =r/100)
1.0833 – 1 = r/100
0.0833 = r/100
r = 8.33%

## 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 = P(R2)/(1002)
100 = P(142)/(1002)
P = (100*1002)/142
P = 1000000/196
P = 5102.04
Now calculate the CI on Rs. 5102.04
A = 5102.04 (1+14/100)3
A = 5102.04 (114/100)3
A = 5102.04 * 1.48
A= 7558.89

## 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

We know that,
(x)1/a = (y)1/b
2(1/8) = 32(1/x)
2(1/8) = 2(5/x)
1/8 = 5/x
x = 40 years

## 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+r1/100) (1+r2/100) (1+r3/100)
Here, r1 = 2% r2 = 4% and p = Rs.10000,
CI = A – P
CI = 10000 (1 + 2/100) (1 + 4/100) – 10000
CI = 10000 * (102/100)(104/100) – 10000
CI = 10000 * (51 * 52/2500) – 10000
CI = 10000 * (2652 / 2500) – 10000
CI = 10000 * (1.06) – 10000
CI = 10608 – 10000
CI = 608
Hence, the required compound interest is Rs. 608.