Question

QUESTION 1

A) Mr Baxter is planning on travelling with his family to the Soccer World Cup semifinals and final in North America in six years time and would like to start saving today towards the cost of the trip. Victory Ltd, an international sports tour operator has estimated that the cost for him and his family in six years time would amount to R 350 000 in total. This would include the cost of the flights, accommodation and stadium tickets. He has approached you, his financial advisor, on the best way to go about saving for this trip.

REQUIRED:
If Mr Baxter could invest a lump sum of R 75 000 today in a fixed deposit offering ten percent (10%), compounded bi‐annually. In addition to this he will save on a monthly basis. Calculate the amount he would then need to deposit monthly at the beginning of each month in an annuity offered by Bucks Assets Managers at an interest rate of eighteen percent (18%) per annum compounded monthly, in order to make up the shortfall.

B) Mr Hamilton would like to purchase a vehicle for his son’s 21st birthday. If the vehicle costs R225 000 and the dealership requires a twenty percent (20%) deposit with monthly repayments at an interest rate of 15% compounded monthly over five years, how much sooner would Mr Hamilton be able to repay the loan agreement if he decided to offer a twenty five percent (25%) deposit and kept the monthly instalments the same as originally calculated with the deposit requested by the dealership.

Answer 1

Part i)

Principal (p) = 75,000; period(n) = 6years*2 = 12 bi-annual; interest rate (r) = 10%/2 = 5%

Fixed deposit maturity value = p*(1+r)^n = 75000*(1+0.05)^12 = 75000*(1.05^12) = 75000*1.795856 = 134,689

Required amount in 6years = 350,000

Maturity value of monthly deposit required (FV) = Required amount in 6years-Fixed deposit maturity value = 350,000 - 134,689 = 215,311

rate (i) per month = 18%/12 = 1.5%; Period in months(m) = 6years*12 = 72months;

FV = Monthly deposit*(1+i)*{[(1+i)^m]-1}/i

215311 = Monthly deposit*(1+0.015)*{[(1+0.015)^72]-1}/0.015

215311*0.015 = Monthly deposit*1.015*{[1.015^72]-1}

3229.665 = Monthly deposit*1.015*1.921157961
Monthly deposit = 3229.665/(1.015*1.921157961)

Monthly deposit = 1,656.26

Part ii)

Total amount = 225,000

Deposit = Total amount*20% = 225,000*20% = 45,000

Principal repayment(p) = Total amount-deposit = 225,000-45,000 = 180,000; Period (n) = 5years *12 = 60months; rate(r) = 15%/12 = 1.25%per month

EMI = P*r*[(1+r)^n]/{[(1+r)^n]-1} = 180,000*0.0125*[(1+0.0125)^60]/{[(1+0.0125)^60]-1} = 2250*(1.0125^60)/[(1.0125^60)-1] = 2250*2.10718135/1.10718135 = 4,282.19

Monthly EMI = 4,282.19

Part iia)

Total amount = 225,000

Deposit = Total amount*25% = 225,000*25% = 56,250

Principal repayment (p) = Total amount-deposit = 225,000-56,250 = 168,750; rate(r) = 15%/12 = 1.25%per month; EMI = 4282.19

EMI = P*r*[(1+r)^n]/{[(1+r)^n]-1}

4282.19 = 168,750*0.0125*[(1+0.0125)^n]/{[(1+0.0125)^n]-1}

4282.19 = 2109.375*(1.0125^n)/[(1.0125^n)-1]

(1.0125^n)/[(1.0125^n)-1] = 4282.19/2109.375 = 2.030075

(1.0125^n) = 2.030075*[(1.0125^n)-1]

(1.0125^n) = 2.030075*(1.0125^n) - 2.030075

2.030075 = 2.030075*(1.0125^n) - (1.0125^n)

2.030075 = 1.030075*(1.0125^n)

(1.0125^n) = 2.030075/1.030075

(1.0125^n) = 1.97

(1.0125^n) = (1.0125^55)

Period = 55months or 4years & 7months