Question

Giulia has just commenced her first professional full-time job in Australia and is looking to save a deposit to purchase a property. She gets paid monthly and is looking to save some of her salary in order to achieve her goal. Her target is to have $120 000 in three years from now and is confident that she can earn 7% p.a. compounded monthly on her savings.

1. How much will Giulia need to save at the end of each month in order to achieve her target in three years?

   Assume three years from now Giulia achieves her target and purchases a home with a twenty-five year loan for $450 000. The interest on the loan is 3.30% p.a. and compounds daily.

2. Calculate Giulia’s monthly repayments on this loan.
3. When Giulia purchased the property it was valued at $550 000. If it is expected to grow at 4% p. for the next twenty-five years, what will be the value of the property twenty-five years from now?

Answer 1

1.
Periodic Annuity Payments=Future Value*periodic rate/((1+periodic rate)^n-1)
=120000*(7%/12)/((1+7%/12)^(12*3)-1)=3005.25162384462

2.
rate compounded monthly=((1+3.3%/365)^(365/12)-1)*12=3.3043921%

Periodic Payment Annuity=Loan*periodic rate/(1-1/(1+periodic rate)^n)
=450000*(3.3043921%)/(1-1/(1+3.3043921%)^(12*25))=2205.87445828788

3.
Future Value=Present Value*(1+r)^t
=550000*(1+4%)^25=1466209.98231808