Reducible Loans 4
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Question 1 of 4
1. Question
Jason took out a loan for `$500 000` and was given the choice to repay it either monthly or fortnightly. If he chooses to pay back monthly, he’ll be paying back `$2539` per month. If he chooses to pay fortnightly, it will be `$1276` per fortnight. What is the difference in total repayments using the two different methods of payment?
- `$` (117816, 117,816)
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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.First, find the total monthly repayments by multiplying the monthly repayment to `12` (number of months in a year) and to the loan duration (in years).
Monthly Repayment `=$2539`Loan Duration `=30` years`$2539xx12xx30` `=` `$914 040` Next, find the total fortnightly repayments by multiplying the fortnightly repayment to `26` (number of fortnights in a year) and to the loan duration (in years).
Fortnightly Repayment `=$1276`Loan Duration `=24` years`$1276xx24xx26` `=` `$796 224` Finally, compute for the savings if the fortnightly payment method is chosen.Years saved:Years if paid monthly `-` Years if paid fortnightly `=` `30-24` `=` `6` years Dollars saved:Total monthly repayments `-` Total fortnightly repayments `=` `$914 040-$796 224` `=` `$117 816` If the loan is paid fortnightly, Jason can save `6` years and `$117 816``$117 816` -
Question 2 of 4
2. Question
In this graph, the balance owing over time is shown for a loan of `$550 000` which is to be repaid in `30` years. Approximately how much is still owing after `10` years?
- `$` (450000, 450,000)
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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.First, find the `10`th year in the graph and draw a vertical line over it until it reaches the red curve.
From the point where the vertical line reaches the red curve, draw a horizontal line until it reaches the loan balance axis.
Since the line stops somewhere between `400 000` and `500 000`, the balance owing after `10` years is approximately `$450 000`.`$450 000` -
Question 3 of 4
3. Question
In this graph, the balance owing over time is shown for a loan of `$550 000` which is to be repaid in `30` years. How much has the loan reduced after `16` years?
- `$` (200000, 200,000)
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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.First, find the `16`th year in the graph.
Draw a vertical line over the `16`th year until it reaches the red curve.
From the point where the vertical line reaches the red curve, draw a horizontal line until it reaches the loan balance axis.
Since the line stops somewhere between `300 000` and `400 000`, the balance left after `16` years is approximately `$350 000`.To find how much was reduced after `16` years, subtract `$350 000` from the principal amountPrincipal Amount `=$550 000``$550 000-$350 000` `=` `$200 000` `$200 000` -
Question 4 of 4
4. Question
In this graph, the balance owing over time is shown for a loan of `$550 000` which is to be repaid in `30` years. After how many years will the loan be half-paid?
- (20) years
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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.First, solve for half of the principal amountPrincipal Amount `=$550 000``$550 000xx1/2` `=` `$275 000` Next, find `$275 000` in the graph and draw a horizontal line across it until it reaches the red curve.
From the point where the horizontal line reaches the red curve, draw a vertical line until it reaches the time axis.
Since the line stops somewhere between `18` and `22`, it will take approximately `20` years for the loan to be half-paid.`20` years