Monday, 24 April 2017

Interest IV - Problems on Interest Compounded Half-yearly and Compound Interest for Fractional time-period.

Quick formulas to solve problems on Interest Compounded Half-yearly and Compound Interest for Fractional time-period

Problems on Interest Compounded Half-yearly and Compound Interest for Fractional time-period 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 half-yearly and Module 6: Compound Interest for Fractional Time Period. 

Modules 1 and 2 are discussed in Interest-II 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 Half-Yearly


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 half-yearly 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.

Let’s have a quick go through at the special cases in which Interest is charged.
Compound Interest
Compound Interest
Compound Interest
Compound Interest
                        
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
Compound Interest
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 half-yearly, What is the amount that has to be paid?

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%

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.
For example, time period = a(b/c) then, the total amount at the end of the period at R% p.a on a period amount "P," will be given as,



We just need to substitute the vales in the formulas to solve the problems.


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)
       = 104(120/100)(105/200)
       = 104(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 Half-yearly and Compound Interest for Fractional time-period 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.

  Compound Interest          

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