Reducible Loans 3
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Question 1 of 5
1. Question
Gian borrows `$315 000` at an interest rate of `5.9%` per annum. It is a reducible loan whereby he pays back `$1272` per fortnight. If the loan was paid over a period of `14` years, find the following:`(i)` Total repayments.`(ii)` Total interest paid.-
`(i) $` (463008, 463,008)`(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)` Find the total repayments.To find the total repayments, multiply the fortnightly repayment to `26` (number of fortnights in a year) and to the loan duration (in years).Fortnightly Repayment `=$1272`Loan Duration `=14` years`$1272xx26xx14` `=` `$463 008` `(ii)` Find the total interest paid.Simply subtract the principal amount from the total repayments.Total Repayment `=$463 008`Principal (`P`) `=$315 000``$463 008-$315 000` `=` `$148 008` `(i) $463 008``(ii) $148 008` -
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Question 2 of 5
2. Question
Gian borrows `$315 000` at an interest rate of `5.9%` per annum. It is a reducible loan whereby he pays back `$1272` per fortnight. If the loan was paid over a period of `14` years, find the equivalent flat interest rate.Round your answer to `1` decimal place- (3.4)`%`
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Flat Interest Rate
`I``=``P``R``N`where:
`I=` Total Interest Paid
`P=` Principal Amount
`R=` Flat Interest Rate
`N=` Number of years of the loanUse the given formula to find `R` or the flat interest rate.Total Interest (from previous question) `=$148 008`Principal Amount (`P`) `=$315 000`Number of years (`N`) `=14``I` `=` `P``R``N` Flat Interest Rate Formula `$148 008` `=` `$315 000``xx``R``xx``14` Substitute values `(148 008)/(315 000xx14)` `=` `R` Leave `R` on one side `0.03356` `=` `R` `R` `=` `3.4%` Convert from decimal to percentage `3.4%` -
Question 3 of 5
3. Question
A loan of `$580 000` is paid over a period of `12` years with an interest rate of `5%` per annum and fortnightly repayments of `$2474`. Find the following:`(i)` Total repayments.`(ii)` Total interest paid.-
`(i) $` (771888, 771,888)`(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)` Find the total repayments.To find the total repayments, multiply the fortnightly repayment to `26` (number of fortnights in a year) and to the loan duration (in years).Fortnightly Repayment `=$2474`Loan Duration `=12` years`$2474xx26xx12` `=` `$771 888` `(ii)` Find the total interest paid.Simply subtract the principal amount from the total repayments.Total Repayment `=$771 888`Principal (`P`) `=$580 000``$771 888-$580 000` `=` `$191 888` `(i) $771 888``(ii) $191 888` -
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Question 4 of 5
4. Question
A loan of `$580 000` is paid over a period of `12` years with an interest rate of `5%` per annum and fortnightly repayments of `$2474`. Find the equivalent flat interest rate.Round your answer to `2` decimal places- (2.76)`%`
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Flat Interest Rate
`I``=``P``R``N`where:
`I=` Total Interest Paid
`P=` Principal Amount
`R=` Flat Interest Rate
`N=` Number of years of the loanUse the given formula to find `R` or the flat interest rate.Total Interest (from previous question) `=$191 888`Principal Amount (`P`) `=$580 000`Number of years (`N`) `=12``I` `=` `P``R``N` Flat Interest Rate Formula `$191 888` `=` `$580 000``xx``R``xx``12` Substitute values `(191 888)/(580 000xx12)` `=` `R` Leave `R` on one side `0.02757` `=` `R` `R` `=` `2.76%` Convert from decimal to percentage `2.76%` -
Question 5 of 5
5. Question
Giselle borrowed `$450 000` to buy a home which will be repaid over `30` years with monthly repayments of `$2416`. After `10` years, she lumps in `$100 000` into the loan and the monthly repayments remain unchanged. The graph below shows the balance owing over the period of the loan. How much did Giselle save by paying a lump sum?
- `$` (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` years, Giselle completed paying off the loan after 21 years.Since `30-21=9`, she saved `9` years by paying the lump sum.Next, multiply the number of years saved to the monthly repayment and `12` (number of months in a year)Years saved `=9`Monthly Repayment `=$2416``9xx$2416xx12` `=` `$260 928` Finally, subtract the lump sum that she paidLump Sum `=$100 000` after `10` years`$260 928-$100 000` `=` `$160 928` `$160 928`