Question

You have approached Commonwealth Bank for a loan to buy a house.
The bank offers you a $500 000 loan, repayable in equal monthly
instalments at the end of each month for the next 30 years.
Required:

a. If the interest rate on the loan is 4.5% per annum, compounded
monthly, what is your monthly repayment (to the nearest
dollar)?

b. What is your weekly payment if you wish to pay weekly
instalments and the interest rate is compounding weekly?

At the end of this month, Leslie will start saving $200 a month
for retirement through his company's superannuation plan. His
employer will contribute an additional $0.50 for every $1.00 that
he saves. He is employed by this firm for 30 more years and earns
an average of 11% monthly compounding on his retirement savings.
Required:

a. How much will Leslie have in his superannuation account 30 years
from now?

b. If at the end of year 20, Leslie voluntarily puts $20 000 in his
superannuation, how much will he has in that account when he
retires?

c. Leslie has a second investment and it will start to pay him $
25,000 next year and after that the payment will grow at 4% each
year for the rest of his life. How much is the present value of
Leslie’s investment payments if the required rate of returns is
8%?

d. How much is the present value of this second investment cash
flow if the payment is the same every year and the rate of return
is the same 8%?

Answer #1

**Question 1:**

**A. Calculation of monthly instalment :**

Loan Amount = $500,000

Interest rate = 4.5% p.a. compounded monthly

Period = 30 years i.e., 360 months

Annuity Factor at the rate 0.375% (4.5/12) for 360 months = 197.361159 [1/(1.00375)1+1/(1.00375)2.......+1/(1.00375)360)

Monthly Instalment = 500000/197.361159

=$2533 per month (approx.)

**B. Calculation of weekly instalment :**

Loan Amount = $500,000

Interest rate = 4.5% p.a. compounded weekly

Period = 30 years i.e., 1560 weeks

Annuity Factor at the rate 0.087% (4.5/52) for 1560 weeks = 853.411099 [1/(1.00087)1+1/(1.00087)2.......+1/(1.00087)1560)

Weekly Instalemnt = 500000/853.411099

=$586 per week (approx.)

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