(May 10, 2012)Outline Question 1 (a)- (c)Question 2 (a)- (c)Question 3 (a)- (d)Question 4 (a)- (d)Question 5 Question 1The aim of this question is to weigh through three options and decide the best form of investment. The three borrowing options offer different rates. The interest rates are nominal meaning that they have not been adjusted to inflation. The effective rate is used in this case since it is more realistic. The interest rates have been compounded. Compounding means that they change with time. This can be daily, monthly, quarterly or annually.
The funding that is needed is $1,000,000 and is required for 5 years. The best option is that which gives rise to the least amount payable at the end of the loan. Option 1: ABC Friendly Finance CompanyThe nominal rate is 10.50% per annum which is compounded daily. ABC Friendly Finance Company effective annual rate of interest: = (1+0.1050/365)^365-1=1.000287671^365-1=1.110693838-1= 0.110693837=11.07%Amount payable after 5 years= P (1+r/n) nt=$1,000,000 (1+ 0.1107/365) 365*5=$1,000,000*(1.0003032881825) =$1,739,184.07Option 2: DEF Commercial Bank LtdThe nominal rate is 10.55% per annum which is compounding quarterly. DEF Commercial Bank Ltd effective annual rate of interest: =(1+0.1055/4)^4-1=1.026375^4-1=1.109747718-1=0.109747717=10.97%Amount payable after 5 years: =$1,000,000 (1+ 0.1097/4) 4*5=$1,000,000*(1.02742520)=$1,717,918.60Option 3: SHARKIES Cheap Loans LtdThe rate used in this option is 9.50% per year (simple interest).
This has been converted to 4.75% per every half year. Therefore, the installments are made in equal ‘six monthly installments’ over the term of the loan. SHARKIES Cheap Loans Ltd effective annual rate of interest: =2*Annual no. of payments*Interest/ (Total no. of payments+1)*Principal=2*2*(95,000*5)/ (2*5+1)*1,000,000= 1,900,000/ (11*1,000,000)=0.1727=17.27%Amount payable after 1 year=$1,000,000 + (1,000,000*0.1727/2*1) = 1,000,000+86,350=$1,086,350Amount payable after 2 years=$1,086,350+86,350=$1,172,700Amount payable after 3 years=$1,172,700+86,350=$1,259,050Amount payable after 4 years=$1,259,050+86,350=$1,345,400Amount payable after 5 years=$1,345,400+86,350=$1,431,750The best source of finance would be from SHARKIES Cheap Loans Ltd.
This is because the amount of loan payable after 5 years would be $1,431,750 which is much less as compared to other sources. For instance, the amount of loan payable when using ABC Friendly Finance Company would be $1,739,184.07 while the amount payable when using DEF Commercial Bank Ltd would be $1,717,918.60. This leaves SHARKIES Cheap Loans Ltd as the cheapest and the best source of financing. b) The effective rate of interest per annum would definitely change if Sharkies CheapLoan Ltd charged an application fee of $1000 payable on day zero of the loan.
This is because fees such as application fees reduce the amount of loan borrowed. Consequently, the rate of interest is expected to increase as the denominator (amount borrowed) reduces. Loan principal=$1,000,000Interest rate=9.50%Application Fee=$1,000Effective amount borrowed= $1,000,000-$1,000=$999,000Interest paid= 0.095*1,000,000=$95,000Effective Interest rate= Interest paid/ Effective amount borrowed=$95,000/$999,000=0.09509=9.51%The effective rate of interest when the client is charged the application fee is slightly higher than when there are no application fees. The change is only slight because the application fee was a mere $1,000 which had little effect on the total amount borrowed. (c) As discussed earlier, nominal interest rate does not take in to account economic factors like the inflation rates.
If inflation rate is accounted in calculation of interest rate, then real interest rate is realized. Real interest rate= Nominal interest rate-Inflation rate