VCE Further Maths Revision 2

A key feature of a perpetuity is that:

• The interest paid is higher than an annuity.

• There are no fees charged.

• The amount in the bank remains constant.

• The interest rate always increases over time.

• The interest rate always decreases over time.

Consider the graph pictured.

The graph could show the value of:

• a piano depreciating at a flat rate of 6% per annum.

• a car depreciating with a reducing balance rate of 6% per annum

• a compound interest investment earning interest at the rate of 6% per annum.

• a perpetuity earning interest at the rate of 6% per annum.

• an annuity investment with additional payments of 6% of the initial investment amount per annum.

The first five terms of a sequence are 2, 6, 22, 86, 342 … The recurrence relation that generates this sequence could be:

• 
• 
• 
• 
• 

Maria would like to purchase a new home. She will establish a loan for $225000 with interest charged at the rate of 3.6% per annum, compounding monthly. Each month, Maria will pay only the interest charged for that month. After three years, the amount that Maria will owe is:

• 73362

• 170752

• 225000

• 239605

• 245865

How much interest is paid per month on the $225000 loan if the interest rate is 3.6% per annum?

• 8100

• -8100

• -675

• 675

• 0.36

Lee borrowed $245 000 to pay for a house. For the first 10 years of the loan, the interest rate was 4.35% per annum, compounding monthly. Lee made monthly repayments of $1800. After 10 years, the interest rate changed. If Lee now makes monthly repayments of $2000, he could repay the loan in a further five years. The new annual interest rate for Lee's loan is closest to

• 0.35%

• 4.1%

• 4.5%

• 4.8%

• 18.7%