How To Solve Compound Interest Problems Quickly
How To Solve Quickly Compound Interest & Definition of Compound Interest
Compound interest is the interest calculated on the original principal and on the accumulated past interest of a deposit or loan.
- Compound interest calculated by multiplying the original principal amount one plus the annual interest rate raised to the number of compound periods minus one.
Basic Formula for the Compound Interest is
A= P(1 + r/n)nt
Where, A = Amount
P = Principal
r = Interest rate(decimal)
n = number of times interest is compounded per unit ‘t’

Type 1: How To Solve Compound Interest Quickly (Yearly, Quarterly, and Half-yearly)
Ques 1.
If a sum of Rs.100 is invested for 10% p.a at CI then the sum of the amount will be Rs.121 in
Options:
A. 2 years
B.1 year
C.1.5 years
D. 3 years
Solution:
We know that, Amount = P (1+r/100)^t
121 = 100 (1 + 10/100)t
121/100 = (11/10) t
(11/10)2 = (11/10) t
t = 2 years
Correct option: A
Ques 2.
Find the CI on Rs. 10,000 in 2 years at 2 % per annum, the interest being compounded half-yearly.
Options:
A. 408
B. 406.04
C. 409.03
D. 405.50
Solution:
According to the question
P =10000, r = 2%, t = 2
We know that,
Amount = P (1+r/2/100)2t
A = 10000 (1+ 2/2/100)4
A = 10000 (1+ 1/100)4
A = 10000 (1+ 0.01)4
A = 10000 (1.01)4
A = 10000 (1.04)
A = 10406.04
Now, CI = A – P
CI = 10406.04 – 10000
CI = 406.04
Correct option: B
Ques 3.
Find the CI on Rs. 2000 in 9 months at 12% p.a. if the interest is calculated quarterly.
Options:
A. 251.01
B. 251
C. 304
D.185.45
Solution:
According to the question,
P = 2000, r = 6%, t = 9 months (3 quarter)
We know that,
Amount = P (1+r/4/100)4t
A = 2000 (1+12/4/100)3
A = 2000 (1+3/100)3
A = 2000 (1+0.03)3
A = 2000 (1.03) 3
A = 2000 (1.09)
A = 2185.45
Now, CI = A – P
CI = 2185.45– 2000 = 185.45
Correct option: D
Type 2: Solve Compound Interest Quickly (Rate of Interest, Time period, Principal)
Ques 1.
The CI on Rs. 20,000 at 6% per annum is Rs. 2472. Find the period (in years):
Options:
Options:
A. 2
B. 4
C. 5
D. 3
Solution:
Amount = 20000 + 2472 = Rs. 22472
Let the time = n years
So, 20000 (1 + 6/100)n = 22472
(106/100)n = 22472/20000 = 11236/10000 = (106/100)2
Therefore, n = 2 years
Correct option: A
Ques 2.
The principal amount is put on CI for two years at 40%. It gets 964 more if the interest is payable half yearly. Calculate the sum.
Options:
A. Rs 8485
B. Rs 8485.91
C. Rs 8480
D. Rs 8455.91
Solution:
Let us assume the Principal as Rs. 100
When compounded annually
A = 100 [1+40/100]^2
A= 196
When compounded half yearly
A = 100[1+40/2/100]^4
A = 100[1+20/100]^4
A = 207.36
Difference, 196 – 144 = 11.36
If difference is 11.36, then Principal = Rs 100
If difference is 964, then Principal = 100/11.36 × 964
P = Rs 8485.91
Correct option: B
Ques 3.
In what time the CI on Rs 800 at 30% pa will amount to Rs.1352 if calculated annually?
Options:
A. 3 years
B. 1.6 years
C. 2 years
D. 5 years
Solution:
We know that,
Amount = P (1+r/100)^t
1352 = 800 (1 + 30/100)^t
1352/800 = (1.3)^t
1.69 = (1.3)^t
1.69 = (1.3)^2
Therefore, t = 2 years
Correct option: C
Type 3: Find sum or rate of interest when compound interest and S.I are given (How To Solve C.I Quickly)
Question 1.
If the difference between compound interest and simple interest on a certain principal amount is Rs 500 at 10% p.a. for 2 years. Then calculate the sum.
Options:
A. 45000
B. 50000
C. 55000
D. 5000
Solution:
Given the difference between SI and CI = 500
Time = 2 years
When the difference between SI and CI is of two years then,
Difference = P(R)²/(100)²
Where P = principal amount, R = rate of interest
According to the question:
500 = P(10^2)/100^2
P = 50,000
Correct option: B
Question 2.
The difference between CI and SI on an amount of Rs. 15,000 for 2 years is Rs. 96. Find the rate of interest?
Options:
A. 8%
B. 5%
C. 4%
D. 3%
Solution:
Difference = P(R^2)/100^2
96 = 15000(R^2)/10000
(96*10000)/15000 = R^2
R^2 = 64
R = 8%
Correct option: A
Question 3.
The difference between CI and SI calculated annually on a certain amount of money for two years at 4% pa is Re. 1. Find the sum:
Options:
A. 600
B. 700
C. 650
D. 625
Solution:
When the difference between SI and CI is of two years then,
Difference = P(R)²/(100)²
Where P = principal amount, R = rate of interest
1 = P(4^2)/100^2
P = 625
Correct option: D
Type 4: When sum of money becomes x time in ‘a’ years and y times in ‘b’ years. (Solve Compound Interest Quickly)
Question 1.
A sum of money borrowed under CI gets double in 5 years. When will it become eight times of itself if the rate of interest remains same?
Options:
A. 15 years
B. 20 years
C. 10 years
D. 5 years
Solution:
We know that,
x^(1/a) = y^(1/b)
2^(1/5) = 8^(1/b)
2^(1/5) = 2^(3/x)
1/5 = 3/x
x = 15 years
Correct option: A
Question 2.
If a certain amount of sum becomes 9 times in 2 years at compound interest, then find out the rate of interest?
Options:
A. 250%
B. 100%
C. 200%
D. 20%
Solution:
We know that,
r = 100 [(A/P)^(1/t) – 1)]
Therefore,
r = 100 (9(1/2) -1)
r = 100 (3-1)= 100*2
r = 200%
Correct option: C
Question 3.
At what rate percentage will certain amount of money become 8 times in three years?
Options:
A. 113. 79%
B. 100%
C. 110. 79%
D. 130%
Solution:
We know that,
r = 100 [(A/P)^(1/t) – 1)
r = 100 (8^(1/3) – 1)
r = 100 * (2-1)
r = 100%
Correct option: B
Type 5: When rates are different for different years (How To solve Compound Interest Quickly)
Question 1.
Ravi took an amount of Rs.20000 as loan at CI charging 5%, 10% and 20% for the 1st year, 2nd year, and 3rd year respectively. Find out the total interest to be paid by Ravi at the end of the 3rd year?
Options:
A. Rs. 7270
B. Rs. 2270
C. Rs. 7720
D. Rs. 7027
Solution:
According to the question,
P = 20000
R = 5%, 10%, and 20%
T= 1, 2, and 3 years
Amount = 20000 [(1+5)/100 * (1+10)/100 * (1+20)/100]
Amount = 20000 [(105/100) * (110/100) * (120/100)]
Amount = 20000 * 1.05 * 1.1 * 1.2
Amount = 27720
We know that, CI = A – P
CI = 27720 – 20000
CI = Rs. 7720
Correct option: C
Question 2.
If the rate of CI for the 1st year is 8%, 2nd year is 10%, and for 3rd year is 15% then find the amount and the CI on Rs 10000 in three years.
Options:
A. 3626
B. 6236
C. 3666
D. 3662
Solution:
We know that, Amount = P (1+r1/100) (1+r2/100) (1+r3/100)
Amount = 10000 (1+8/100) (1+10/100) (1+15/100)
Amount = 10000 (1.08) (1.1) (1.15)
Amount = 13662
Now, CI = amount –principal
CI = 13662 – 10000
CI = 3662
Correct option: D
Question 3.
Karan bought a bike of Rs. 60000 by paying cash. He borrowed the cash from his friend at rate of interest 5% for the 1st year and 15% for the 2nd year. Find out the total amount he has to pay after 2 years to his friend.
Options:
A. Rs. 72450
B. Rs. 74250
C. Rs. 72540
D. Rs. 75420
Solution
We know that, Amount = P (1+r1/100) (1+r2/100)
Amount after two years = 60000 (1 + 5/100) (1 + 15/100)
Amount after two years = 60000 * 1.05 * 1.15
Amount after two years = Rs. 72450
Correct Option: A
- Read Also – Formulas to solve compound interest questions
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