Quick formulas to solve problems on Interest Compounded Halfyearly and Compound Interest for Fractional timeperiod
Problems on Interest Compounded Halfyearly and Compound Interest for Fractional timeperiod are asked in the Quantitative Aptitude section of SBI PO, IBPS and SSC exam. These problems require little tips and tricks in order to solve them. This post is divided into two parts. Module 5: Interest compounded halfyearly and Module 6: Compound Interest for Fractional Time Period.
Modules 1 and 2 are discussed in InterestII and Modules 3 and 4 are discussed in Interest III  Do have a glance at them to master the concept of Simple Interest and Compound Interest.
Modules 1 and 2 are discussed in InterestII and Modules 3 and 4 are discussed in Interest III  Do have a glance at them to master the concept of Simple Interest and Compound Interest.
Module 5: Interest Compounded HalfYearly
Ram: Hey (Enters into a bank and meets Rajah who is a clerk)
Rajah: How can I help you sir?
Ram: I want to apply for a personal loan. What is the rate of interest that you charge?
Rajah: Sir, the personal loan is charged at 10%p.a compounded half yearly?
Ram: Thanks, (Confused)what is Interest Compounded at halfyearly means?
Are you confused like Ram? Do you also get stuck at a point where Interest is Compounded Half yearly. Don't worry, This module deals with the concept of Interest Compounded on Half yearly basis.
The table shows how rate of interest changes according to its time period.
CASES
YEARLY
HALF YEARLY
QUARTERLY
BIENNIALLY
P
10000
10000
10000
10000
T
2(Time Period)
4(Time Period)
8(Time Period)
1(Time Period)
R
20%p.a
10%
5%
40%
CI
P[{(1+ R)/100)}^{T}1]
P[{(1+ R)/100}^{T}1]
P[{(1+ R)/100}^{T}1]
P[{(1+ R)/100}^{T}1]
A
P[(1+ R)/100]^{T}
P[(1+ R)/100]^{T}
P[(1+ R)/100]^{T}
P[(1+ R)/100]^{T}
Example 1: Module 5 Interest Compounded Half yearly
Problem: A sum of Rs.40000 is invested for 18 months at 20%p.a on compound Interest. If the Interest is Compounded halfyearly, What is the amount that has to be paid?
Rajah: How can I help you sir?
Ram: I want to apply for a personal loan. What is the rate of interest that you charge?
Rajah: Sir, the personal loan is charged at 10%p.a compounded half yearly?
Ram: Thanks, (Confused)what is Interest Compounded at halfyearly means?
Are you confused like Ram? Do you also get stuck at a point where Interest is Compounded Half yearly. Don't worry, This module deals with the concept of Interest Compounded on Half yearly basis.
CASES

YEARLY

HALF YEARLY

QUARTERLY

BIENNIALLY

P

10000

10000

10000

10000

T

2(Time Period)

4(Time Period)

8(Time Period)

1(Time Period)

R

20%p.a

10%

5%

40%

CI

P[{(1+ R)/100)}^{T}1]

P[{(1+ R)/100}^{T}1]

P[{(1+ R)/100}^{T}1]

P[{(1+ R)/100}^{T}1]

A

P[(1+ R)/100]^{T}

P[(1+ R)/100]^{T}

P[(1+ R)/100]^{T}

P[(1+ R)/100]^{T}

Regular Method:
Solution:
Step 1:
Given Data

Half Yearly Compounding
 
P

40000

40000

T

18 months

3 (18/6)

R

20% p.a

10%

Step 2:
Compound Interest = P[{(1+ R)/100)^{T}}1]
Compound Interest = 40000[{(1+ 10)/100)^{3}}1]
= 40000[{(110)/100)^{3}}1]
= 40000[{(1331000)/1000000)}1]
= 400000[(1331000  1000000)/1000000]
= 400000[331000/1000000]
= 13240
Therefore, Compound Interest is Rs.13240/
Smart Method:
Solution:
Step 1:
First, we need to find the effective percentage of the Compound Interest.
 So, Effective percentage the end of the year,
Effective
Percentage of first 2 years.
(a + b + ab)/100
a = 10
b = 10
5 + 10 +[(10+10)/100] =
21%
Effective
Percentage of first 2 years Interest+3rd years percentage.
(a + b + ab)/100)
a = 21
b = 10
21 + 10
+[(21+10)/100]=
33.1%
Compound
Interest = 33.1%
Effective
Percentage of first 2 years.

(a + b + ab)/100

a = 10
b = 10

5 + 10 +[(10+10)/100] =

21%

Effective
Percentage of first 2 years Interest+3rd years percentage.

(a + b + ab)/100)

a = 21
b = 10

21 + 10
+[(21+10)/100]=

33.1%

Compound
Interest = 33.1%
Step 2:
By the Concept of Ratio and Equivalent Proportion we cross multiply Principal Amount with Compound Interest effective percentage and Principal Percentage with unknown Compound interest amount to find the Compound Interest.
Compound Interest = 13240/
Therefore, Compound Interest is Rs.13240/
Module 6: Compound Interest for Fractional Time Period
Module 6 deals with the problems in which the given time period is in fractions.
Example 1: Module 6  Compound Interest for Fractional Time Period
Problem: An amount of Rs.10000 was deposited in a bank for a period of 27 months at the rate of 20%p.a on compound Interest. What will the amount received on maturity?
Solution:
Step 1:
P = 10000
R=20% p.a
T= 27 months
2 years+ 3 months = 2 years + (1/4)y
Step 2:
A = P[ (1+R/100)^{a}(1+(b/c)R/100)]
A = 10000[(1 + 20/100)^{2}(1+(1/4)20/100)
= 10^{4}(120/100)(105/200)
= 10^{4}(36/25)(21/20)
= 15120
Therefore, The compound Interest we get at the end of 2 years and 3 months is Rs.15210/
Do write in the comment Section on how this post helped you to solve problems with ease on Interest Compounded Halfyearly and Compound Interest for Fractional timeperiod and do remember to use these smart methods every time you practice or solve problems based on Simple Interest and Compound Interest.
Stay tuned for our next post.
Problem: An amount of Rs.10000 was deposited in a bank for a period of 27 months at the rate of 20%p.a on compound Interest. What will the amount received on maturity?
Stay tuned for our next post.
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