Disussion Topic: Compounding and Annuities
Mr. Ahmed has just retired from a government job and he has received a handsome amount as his gratuity. He has a plan to invest his money received from gratuity for which he is in search of a profitable investment option. One of his friends has suggested him three investment options considering his aim of investment. Mr. Ahmed is not aware of investment dynamics (the risk and return) therefore he needs help from someone to choose among the three available investment options. Being a student of financial management you are required to help Mr. Ahmed in choosing the best option as an investment for 10 years based on the principle of “time value of money”. Following is the information available about three investment options:
Option 1: Deposit an amount of Rs. 120,000 at beginning of each year for the next 10 years in a saving account at ABC bank which provides 12% interest rate compounded annually.
Option 2: Deposit an amount of Rs. 50,000 at end of each year for the next 10 years in saving account of M Bank which provides 10% interest rate compounded quarterly.
Option 3: Deposit an amount of Rs. 100,000 at end of each year for the next 10 years in a saving account at N&P bank which provides 10% interest rate compounded semi-annually.
Required:
Using a common base of comparison, you are required to help Mr. Ahmed in estimating what will he get in future from the three investment options and which option he should select to get the maximum benefit from the investment. Calculations (formula and detailed working) are mandatory for each investment option. Decision to select the best option should be based on your calculations.
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Dear Brother plz share solution today is last date of submittion
FV=PV(1+i)n
Option 1
FV=120000(1+12%)10=373200
Option 2
FV=PV(1+i/m)n*m
FV=50000(1+10%/4)10*4=134500
Option 3
FV=100000(1+10%/2)10*2=265000
option 1 must be opted
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Option 1: Deposit an amount of Rs. 120,000 at beginning of each year for the next 10 years in a saving account at ABC bank which provides 12% interest rate compounded annually.
Solution:
Cash Deposit CCF=120,000
No of years (m*n) =10
Interest rate (i/m) =12%
Compound annually =Nill
FV=CCF
Option 2: Deposit an amount of Rs. 50,000 at end of each year for the next 10 years in saving account of M Bank which provides 10% interest rate compounded quarterly.
Solution:
Cash Deposit CCF=50,000
No of years (m*n) =10
Interest rate (i/m) =10%
Compound Quarterly =4
Option 3: Deposit an amount of Rs. 100,000 at end of each year for the next 10 years in a saving account at N&P bank which provides 10% interest rate compounded semi-annually.
Solution:
Cash Deposit CCF=100,000
No of years (m*n) =10
Interest rate (i/m) =10%
Compound semi-annually =2
Reason:
Option 2 is best because in option 2 profit value is high.
Option A
Cash Deposited CCF = 120,000
No of year (mxn) =10
interest Rate (i/m) = 12%
Compound annually = Nil
Formula
FV = CCF {[1+(i/m)] ^{mxn} -1} / (i/m)
FV = CFF {[1+12%]^{10} -1}/ (0.12)
FV = CFF {3.10584 -1}/ (0.12)
FV = CFF (17.5487)
FV = 120,000 (17.5487)
FV = 21,05844 Answer
Option B
Cash Deposited CCF = 50,000
No of year (mxn) =10
interest Rate (i/m) = 10%
Compound quarterly= 4
Formula
FV = CCF {[1+(i/m)] ^{mxn} Quaretly-1} / (i/m)
FV = CCF {[+ (10%/4)]^{10*4} -1}/ (10%/4)
FV = CCF {[1.025]^{40} -1}/ (0.025)
FV = CCF {[2.685063 -1}/ (0.025)
FV = CFF {67.40252}
FV = 50,000 * 67.40252
FV = 3370126 Answer
Option C
Cash Deposited CCF = 100,000
No of year (mxn) =10
interest Rate (i/m) = 10%
Compound semi-annually= 2
Formula
FV = CCF {[1+(i/m)] ^{mxn} Quaretly-1} / (i/m)
FV = CCF {[1+(10%/2)]^{10*2} -1}/ (10%/2)
FV = CCF {[1.05]^{20} -1}/(0.05)
FV = CFF {1.65329}/ (0.05)
FV = 100,000 * 33.0658
FV = 33,06580 Answer
Reason:
Option 2 is best because in option 2 profit value is high.
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