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