Reducible Loans 3

Years

Year 10

Consumer Maths

Reducible Loans

Reducible Loans 3

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Question 1 of 5

1. Question
Gian borrows $$ 315 000$ $$315 000$ at an interest rate of $5.9 %$ $5.9%$ per annum. It is a reducible loan whereby he pays back $$ 1272$ $$1272$ per fortnight. If the loan was paid over a period of $14$ $14$ years, find the following:

$(i)$ $(i)$ Total repayments.

$(i i)$ $(ii)$ Total interest paid.
- $(i) $$ $(i) $$ (463008, 463,008)
  
  $(i i) $$ $(ii) $$ (148008, 148,008)
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A Reducible Loan is a loan where the interest is paid on the balance owing, or the remaining amount of the loan that is yet to be paid.

$(i)$ $(i)$ Find the total repayments.

To find the total repayments, multiply the fortnightly repayment to $26$ $26$ (number of fortnights in a year) and to the loan duration (in years).

Fortnightly Repayment $= $ 1272$ $=$1272$

Loan Duration $= 14$ $=14$ years

$$ 1272 \times 26 \times 14$ $$1272xx26xx14$ $=$ $=$ $$ 463 008$ $$463 008$

$(i i)$ $(ii)$ Find the total interest paid.

Simply subtract the principal amount from the total repayments.

Total Repayment $= $ 463 008$ $=$463 008$

Principal ( $P$ $P$ ) $= $ 315 000$ $=$315 000$

$$ 463 008 - $ 315 000$ $$463 008-$315 000$ $=$ $=$ $$ 148 008$ $$148 008$

$(i) $ 463 008$ $(i) $463 008$

$(i i) $ 148 008$ $(ii) $148 008$

Question 2 of 5

Gian borrows

$ 315 000

$$315 000$ at an interest rate of

5.9 %

$5.9%$ per annum. It is a reducible loan whereby he pays back

$ 1272

$$1272$ per fortnight. If the loan was paid over a period of

14

$14$ years, find the equivalent flat interest rate.

Round your answer to

1

$1$ decimal place

(3.4) $%$ $%$

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Flat Interest Rate

$I$ $I$

=

$=$ $P$ $P$ $R$ $R$ $N$ $N$

where:

I =

$I=$ Total Interest Paid

P =

$P=$ Principal Amount

R =

$R=$ Flat Interest Rate

N =

$N=$ Number of years of the loan

Use the given formula to find $R$ $R$ or the flat interest rate.

Total Interest (from previous question)

= $ 148 008

$=$148 008$

Principal Amount (

P

$P$ )

= $ 315 000

$=$315 000$

Number of years (

N

$N$ )

= 14

$=14$

$I$ $I$	$=$ $=$	$P$ $P$ $R$ $R$ $N$ $N$	Flat Interest Rate Formula
$$ 148 008$ $$148 008$	$=$ $=$	$$ 315 000$ $$315 000$ $\times$ $xx$ $R$ $R$ $\times$ $xx$ $14$ $14$	Substitute values

$\frac{148 008}{315 000 \times 14}$ $(148 008)/(315 000xx14)$	$=$ $=$	$R$ $R$	Leave $R$ $R$ on one side

$0.03356$ $0.03356$	$=$ $=$	$R$ $R$
$R$ $R$	$=$ $=$	$3.4 %$ $3.4%$	Convert from decimal to percentage

3.4 %

$3.4%$

Question 3 of 5

3. Question
A loan of $$ 580 000$ $$580 000$ is paid over a period of $12$ $12$ years with an interest rate of $5 %$ $5%$ per annum and fortnightly repayments of $$ 2474$ $$2474$ . Find the following:

$(i)$ $(i)$ Total repayments.

$(i i)$ $(ii)$ Total interest paid.
- $(i) $$ $(i) $$ (771888, 771,888)
  
  $(i i) $$ $(ii) $$ (191888, 191,888)
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A Reducible Loan is a loan where the interest is paid on the balance owing, or the remaining amount of the loan that is yet to be paid.

$(i)$ $(i)$ Find the total repayments.

To find the total repayments, multiply the fortnightly repayment to $26$ $26$ (number of fortnights in a year) and to the loan duration (in years).

Fortnightly Repayment $= $ 2474$ $=$2474$

Loan Duration $= 12$ $=12$ years

$$ 2474 \times 26 \times 12$ $$2474xx26xx12$ $=$ $=$ $$ 771 888$ $$771 888$

$(i i)$ $(ii)$ Find the total interest paid.

Simply subtract the principal amount from the total repayments.

Total Repayment $= $ 771 888$ $=$771 888$

Principal ( $P$ $P$ ) $= $ 580 000$ $=$580 000$

$$ 771 888 - $ 580 000$ $$771 888-$580 000$ $=$ $=$ $$ 191 888$ $$191 888$

$(i) $ 771 888$ $(i) $771 888$

$(i i) $ 191 888$ $(ii) $191 888$

Question 4 of 5

A loan of

$ 580 000

$$580 000$ is paid over a period of

12

$12$ years with an interest rate of

5 %

$5%$ per annum and fortnightly repayments of

$ 2474

$$2474$ . Find the equivalent flat interest rate.

Round your answer to

2

$2$ decimal places

(2.76) $%$ $%$

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Flat Interest Rate

$I$ $I$

=

$=$ $P$ $P$ $R$ $R$ $N$ $N$

where:

I =

$I=$ Total Interest Paid

P =

$P=$ Principal Amount

R =

$R=$ Flat Interest Rate

N =

$N=$ Number of years of the loan

Use the given formula to find $R$ $R$ or the flat interest rate.

Total Interest (from previous question)

= $ 191 888

$=$191 888$

Principal Amount (

P

$P$ )

= $ 580 000

$=$580 000$

Number of years (

N

$N$ )

= 12

$=12$

$I$ $I$	$=$ $=$	$P$ $P$ $R$ $R$ $N$ $N$	Flat Interest Rate Formula
$$ 191 888$ $$191 888$	$=$ $=$	$$ 580 000$ $$580 000$ $\times$ $xx$ $R$ $R$ $\times$ $xx$ $12$ $12$	Substitute values

$\frac{191 888}{580 000 \times 12}$ $(191 888)/(580 000xx12)$	$=$ $=$	$R$ $R$	Leave $R$ $R$ on one side

$0.02757$ $0.02757$	$=$ $=$	$R$ $R$
$R$ $R$	$=$ $=$	$2.76 %$ $2.76%$	Convert from decimal to percentage

2.76 %

$2.76%$

Question 5 of 5

5. Question
Giselle borrowed $$ 450 000$ $$450 000$ to buy a home which will be repaid over $30$ $30$ years with monthly repayments of $$ 2416$ $$2416$ . After $10$ $10$ years, she lumps in $$ 100 000$ $$100 000$ into the loan and the monthly repayments remain unchanged. The graph below shows the balance owing over the period of the loan. How much did Giselle save by paying a lump sum?
- $$$ $$$ (160928, 160,928)
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A Reducible Loan is a loan where the interest is paid on the balance owing, or the remaining amount of the loan that is yet to be paid.

A Lump Sum is a single payment made in place of supposed multiple smaller payments.

First, observe the graph and find how many years worth of loan repayments she saved by paying a lump sum.

Notice that instead of finishing after $30$ $30$ years, Giselle completed paying off the loan after 21 years.

Since $30 - 21 = 9$ $30-21=9$ , she saved $9$ $9$ years by paying the lump sum.

Next, multiply the number of years saved to the monthly repayment and $12$ $12$ (number of months in a year)

Years saved $= 9$ $=9$

Monthly Repayment $= $ 2416$ $=$2416$

$9 \times $ 2416 \times 12$ $9xx$2416xx12$ $=$ $=$ $$ 260 928$ $$260 928$

Finally, subtract the lump sum that she paid

Lump Sum $= $ 100 000$ $=$100 000$ after $10$ $10$ years

$$ 260 928 - $ 100 000$ $$260 928-$100 000$ $=$ $=$ $$ 160 928$ $$160 928$

$$ 160 928$ $$160 928$

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Quiz summary

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1. Question

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2. Question

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Flat Interest Rate

3. Question

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4. Question

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Flat Interest Rate

5. Question

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