Reducible Loans 1
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Question 1 of 4
1. Question
Chen borrows `$17000` for his holiday. This loan has an interest rate of `9.5%` per annum and monthly repayments of `$427` for a period of `4` years. Calculate the monthly interest rate as a decimal to `8` places.- (0.00791667)
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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, summarise the data given in the problem.Principal (`P`) `=$17000`Monthly Repayment `=$427`Loan Duration `=4` yearsInterest (`I`) `=9.5%` per annumSolve for the monthly interest rate by dividing `I` by `12`.`9.5%-:12` `=` `9.5/100-:12` Convert from percentage to decimal `=` `0.007916666dot6` Use the calculator to solve `=` `0.00791667` Round off to `8` decimal places `0.00791667` -
Question 2 of 4
2. Question
Chen borrows `$17000` for his holiday. This loan has an interest rate of `9.5%` per annum and monthly repayments of `$427` for a period of `4` years. The table below sets out his monthly repayment schedule for the first three months. Find the missing values `A, B` and `C`.Month Principal (`P`) Interest (`I`) `P` and `I` `P+I-R` `1` `17000` `134.58` `17134.58` `16707.58` `2` `16707.58` `A` `16839.85` `16412.85` `3` `16412.85` `129.94` `16542.79` `B` Sum `C` Round off answers to `2` decimal places-
`A=$` (132.27)`B=$` (16115.79)`C=$` (396.79)
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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.Reducible Loan TableMonth Principal (`P`) Interest (`I`) `P` and `I` `P+I-R` Remaining loan amount Interest amount for the month Principal `+` Interest Principal `+` Interest `-` Repayment Finding `A`First, summarise the data given in the problem.Principal (`P`) `=$17000`Monthly Repayment `=$427`Loan Duration `=4` yearsInterest (`I`) `=9.5%` per annumInterest per month `=0.00791667` (from last question)In the table, `A` is the interest paid in the `2`nd month.To solve this, multiply the monthly interest rate to that month’s principal value.Interest per month `=0.00791667` (from last question)Principal amount for `2`nd month `=16707.58``A` `=` `0.00791667xx16707.58` `A` `=` `$132.27` Month Principal (`P`) Interest (`I`) `P` and `I` `P+I-R` `1` `17000` `134.58` `17134.58` `16707.58` `2` `16707.58` `132.27` `16839.85` `16412.85` `3` `16412.85` `129.94` `16542.79` `B` Sum `C` Finding `B`From the table, `B` is the `P+I-R` in the `3`rd month.To solve this, simply subtract the monthly repayment from the `P` and `I` for that month.Monthly Repayment `=$427``P` and `I` (`3`rd month) `=$16542.79``B` `=` `$16542.79-$427` `B` `=` `$16115.79` Month Principal (`P`) Interest (`I`) `P` and `I` `P+I-R` `1` `17000` `134.58` `17134.58` `16707.58` `2` `16707.58` `132.27` `16839.85` `16412.85` `3` `16412.85` `129.94` `16542.79` `16115.79` Sum `C` Finding `C`From the table, `C` is the sum of the interest paid in the first three months.`I` (`1`st month) `=$134.58``I` (`2`nd month) `=$132.27``I` (`3`rd month) `=$129.94``C` `=` `134.58+132.27+129.94` `C` `=` `$396.79` Month Principal (`P`) Interest (`I`) `P` and `I` `P+I-R` `1` `17000` `134.58` `17134.58` `16707.58` `2` `16707.58` `132.27` `16839.85` `16412.85` `3` `16412.85` `129.94` `16542.79` `16115.79` Sum `396.79` `A=$132.27``B=$16115.79``C=$396.79` -
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Question 3 of 4
3. Question
Constance borrows `$22000` from the bank to buy office equipment. The interest on the loan is charged at `5.9%` per annum which she has to pay at the end of every month. She made repayments of `$516` every month for a period of `4` years. The table below sets out her monthly repayment schedule for the first four months. Find the missing values `x, y` and `z`.Month Principal (`P`) Interest (`I`) `P` and `I` `P+I-R` `1` `x` `108.17` `22108.17` `21592.17` `2` `21592.17` `y` `21698.33` `21182.33` `3` `21182.33` `104.15` `21286.48` `20770.48` `4` `20770.48` `102.12` `20872.60` `z` Round off answer to `2` decimal places-
`x=$` (22000, 22,000)`y=$` (106.16)`z=$` (20356.60, 20356.6, 20,356.60, 20,356.6)
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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.Reducible Loan TableMonth Principal (`P`) Interest (`I`) `P` and `I` `P+I-R` Remaining loan amount Interest amount for the month Principal `+` Interest Principal `+` Interest `-` Repayment Finding `x`First, summarise the data given in the problem.Principal (`P`) `=$22000`Interest (`I`) `=5.9%` per annumLoan Duration `=4` yearsMonthly Repayment `=$516`In the table, `x` is the principal amount in the `1`st month.Since it has just been the start of the loan, that means:`x=$22000`Month Principal Interest `P` and `I` `P+I-R` `1` `22000` `108.17` `22108.17` `21592.17` `2` `21592.17` `y` `21698.33` `21182.33` `3` `21182.33` `104.15` `21286.48` `20770.48` `4` `20770.48` `102.12` `20872.60` `z` Finding `y`From the table, `y` is the interest amount in the `2`nd month.Solve for the monthly interest rate by dividing `I` by `12`.Interest (`I`) `=5.9%` per annum/year`5.9%-:12` `=` `5.9/100-:12` Convert from percentage to decimal `=` `0.059-:12` Move decimal `2` places to the left `=` `0.0049166667` Multiply the monthly interest rate to the `2`nd month’s principal amount`2`nd month Principal Amount `=$21592.17``y` `=` `0.0049166667xx21592.17` `=` `$106.16` Month Principal Interest `P` and `I` `P+I-R` `1` `22000` `108.17` `22108.17` `21592.17` `2` `21592.17` `106.16` `21698.33` `21182.33` `3` `21182.33` `104.15` `21286.48` `20770.48` `4` `20770.48` `102.12` `20872.60` `z` Finding `z`From the table, `z` is the `P+I-R` for the `4`th month.`P` and `I` (`4`th month) `=$20872.60``R` (Monthly Repayment) `=$516``P+I-R` `=` `20872.60-516` `z` `=` `$20356.60` Month Principal Interest `P` and `I` `P+I-R` `1` `22000` `108.17` `22108.17` `21592.17` `2` `21592.17` `106.16` `21698.33` `21182.33` `3` `21182.33` `104.15` `21286.48` `20770.48` `4` `20770.48` `102.12` `20872.60` `20356.60` `x=$22000``y=$106.16``z=$20356.60` -
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Question 4 of 4
4. Question
Constance borrows `$22000` from the bank to buy office equipment. The interest on the loan is charged at `5.9%` per annum which she has to pay at the end of every month. She made repayments of `$516` every month for a period of `4` years. What is the total amount that Constance paid over the loan period?- `$` (24768, 24,768)
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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.To find the total repayments, multiply the monthly repayment to `12` and to the loan duration (in years).Monthly Repayment `=$516`Loan Duration `=4` years`$516xx12xx4` `=` `$24 768` `$24 768`