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1)Your business has just taken out a 1-year instalment loan for R72,500 at a nominal rate of 11
1)Your business has just taken out a 1-year instalment loan for R72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal? a. 73.67% b. 77.55% c. 81.63% d. 85.93% e. 90.45% (2) 3.4 You wish to purchase an asset for R200 000. The finance company requires a 20% deposit. The financed portion is to be repaid, monthly, over 5 years at an annual interest rate of 24% compounded monthly 3.4.1 If payments are to be suspended for the 2nd year of the loan, and then trebled after that, determine the initial (first) payment to repay the loan in 5 years. (2) 3.4.2 If payments are set to grow by 1% a month from the 2nd month, what would your initial (first) payment be to repay the loan in 5 years?
2)Use the following graph to answer CFA Problems 4 and 5. Expected Return, En G.4 H 3 Capital Allocation Line (CAL) 2 Risk, o 4. Which indifference curve represents the greatest level of utility that can be achieved by the investor? 5. Which point designates the optimal portfolio of risky assets?
Expert Solution
1.
Solution to first Question:
Solution is e) 90.45%
Equated Monthly Installment = P * r *[ (1+r)n / ((1+r)n - 1) ]
where,
P= Principal Loan Amount
r= rate of interest calculated on monthly basis
n= loan term / tenure / duration in number of months
Applying the values in this question,
P = R72500
r = 11% / 12
n = 12 months
Therefore,
EMI = 72500 * (11%/12) * [ (1+ (11%/12))12 / ((1+(11%/12))12 -1) ]
= 664.5833 * [ 1.115719 / 0.115719 ]
= 664.5833 * 9.641635
= 6407.67
1st Installment:
Interest payment = R72500 * 11%/12
= 664.5833
EMI = 6407.67
Principal Repayment at the end of 1st month = EMI- Interest payment for the first month
= 6407.67-664.5833
= 5743.0867
Balance of loan at the end of first month = 72500 - 5743.0867
= 66756.9133
2nd Installment:
Balance of loan at the end of first month = R66756.9133
Interest Payment = 66756.9133 * 11%/12
= 611.94
Principal Repayment at the end of 2nd month = EMI- Interest payment for the first month
= 6407.67 - 611.94
= 5795.73
Percentage of the 2nd monthly payment towards the principal = (Principal repayment / EMI )*100
= 5795.73 / 6407.67
= 90.45%
The repayment schedule of loan is attached below for your reference:
please see the attached file.
2.
4. Utility equation ;
U=E(r)-0.5A*(S^2)
U=Utility
A=Degree of Risk Aversion
E(r)=Expected Portfolio Return
S=Portfolio Standard Deviation
Indifference curves are the curves passing through points of constant utility
As the Return increases , utility increases
As Standard deviation decreases, utility increases
Hence maximum utility will be obtained with highest return and lowest standard deviation
Indifference curve 4(GH) represents the greatest level of Utility that can be achieved by the investor
5.The optimal risky portfolio is the portfolio that provides highest Utility
In this case Point F on the Capital Allocation Line (CAL) designates the optimal portfolio of risky assets
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