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AustraliaVIC
VCE 12 General 2023

6.02 Reducing balance loans with technology

Interactive practice questions

Derek borrows $\$50000$$50000 at a rate of $9%$9% (per annum) reducible interest compounded quarterly. At the end of each quarter he makes a repayment of $\$1800$$1800.

We will use the financial solver on your CAS calculator to determine the length of the loan.

a

Which variable on the CAS calculator do we want to solve for?

Pmt

A

I%

B

N

C

PV

D

FV

E
b

Fill in the value for each of the following:

I%: $\editable{}$

PV: $\editable{}$

Pmt: $\editable{}$

FV: $\editable{}$

PpY: $\editable{}$

CpY: $\editable{}$

c

Hence, state after how many quarters the loan will be repaid.

Easy
2min

Xanthe borrows $\$32000$$32000 at a rate of $6.5%$6.5% (per annum) reducible interest compounded monthly. At the end of each month she makes a repayment of $\$380$$380

We will use the financial solver on your CAS calculator to determine the length of the loan.

Easy
4min

Aaron borrows $\$15000$$15000 to buy a car. He is charged $6.8%$6.8% reducible interest compounded monthly.

We will use the financial solver on your CAS calculator to determine what his monthly repayments will be if he wishes to pay off the loan in $3$3 years.

Easy
2min

Mr and Mrs Gwen held a mortgage for $25$25 years. Over that time they made monthly repayments of $\$4500$$4500 and were charge a fixed interest rate of $4.4%$4.4% per annum, compounded monthly.

We will use the financial solver on your CAS calculator to determine how much they initially borrowed.

Easy
2min
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Outcomes

U3.AoS2.3

the concepts of financial mathematics including simple and compound interest, nominal and effective interest rates, the present and future value of an investment, loan or asset, amortisation of a reducing balance loan or annuity and amortisation tables

U3.AoS2.8

use a table to investigate and analyse on a step–by-step basis the amortisation of a reducing balance loan or an annuity, and interpret amortisation tables

U3.AoS2.4

the use of first-order linear recurrence relations to model compound interest investments and loans, and the flat rate, unit cost and reducing balance methods for depreciating assets, reducing balance loans, annuities, perpetuities and annuity investments

U3.AoS2.9

use technology with financial mathematics capabilities, to solve practical problems associated with compound interest investments and loans, reducing balance loans, annuities and perpetuities, and annuity investments

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