| Reducible loans. |
1. Barbara has taken out a personal loan for $15,000 at 6% p.a. monthly reducible repayable over 3 years. The loan will be repaid by Barbara depositing $457 at the end of each month.
(i) What is Barbara's monthly interest rate?
(ii) How much does Barbara owe after the first amount of interest is added?
(iii) How much does Barbara owe after she makes her first repayment?
Answer.(i) Monthly interest rate is 0.5% = 0.005.
(ii) She owes $14,618 after the 1st repayment. |
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2. Chris and Meg wish to do some home renovations and take out a loan for $30,000 over 5 years at 3% p.a. They repay the loan by depositing $539 at the end of each month.
(i) What is their monthly interest rate?
(ii) How much do they still owe after the first payment?
(iii) How much do they still owe after their second payment?
(iv) How much interest have they paid after the second repayment?
Answer.(i) Monthly interest rate is 0.25% = 0.0025.
(ii) They owe $29,536 after the 1st repayment.
(iii) They owe $29,070.84 after the 2nd repayment.
(iv) They have paid $148.84 in interest. |
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3. The following table summarises the course of repayments on a home loan over the first three months of a loan:
| Amount borrowed: |
$300,000 |
This table assumes the same number of days each month.
Simple interest for each calculation:
I = Pr or I = P×(r/12) |
| Annual interest rate (r): |
7% |
| Monthly repayment (R): |
$2000 |
| Month (n) |
Principal (P) |
Interest (I) |
P + I |
P + I - R |
| 1 |
$300,000.00 |
$1,750.00 |
$301,750.00 |
$299,750.00 |
| 2 |
$299,750.00 |
$1,748.54 |
$301,498.54 |
$299,498.54 |
| 3 |
$299,498.54 |
A |
B |
C |
(i) Explain how the interest for the first month of $1,750 is calculated.
(ii What is the balance of the loan at the end of the first month?
(iii) Why is the interest for month 2 less than the interest for
month 1?
(iv) How much of the repayment made in month 2 was used to pay down the amount owing?
(v) Complete the table by calculating the values for the cells
marked A, B and C.
(vi) By how much has the loan been reduced by the end of month 3?
Answer.(i) Interest = $300,000 × (7%÷12).
(ii) Loan balance is $299,750.
(iii) Month 3 interest is calculated on a lower Principal.
(iv) A = $1,747.07
B = $301,245.61
C = $299,245.61.
(vi) Reduced by $754.39. |
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4. Danielle develops the spreadsheet shown below on Excel so that she can monitor her loan month by month.
| Amount borrowed: |
$45,000 |
This table assumes each month is one-twelfth. of a year.
Simple interest for each calculation:
I = Pr or I = P×(r/12) |
| Annual interest rate (r): |
8% |
| Monthly repayment (R): |
$500 |
| Month (n) |
Principal (P) |
Interest (I) |
P + I |
P + I - R |
| 1 |
$45,000.00 |
$300.00 |
$45,300.00 |
$44,800.00 |
| 2 |
$44,800.00 |
$298.67 |
$45,098.67 |
$44,598.67 |
| 3 |
A |
B |
C |
D |
(i) Find the values of A, B, C and D.
(ii) How much has Danielle's loan been drawn down by the end of month 3?
(iii) How much interest has Danielle paid over the first three months of her loan?
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| Loan repayment tables. |
5. Will is considering a loan to enable him to do various things in the future. Some of his plans are short term while other activities are longer term.
The lending institution provides the following table showing the fortnightly repayments required by Will to repay a loan at 11.5% p.a. with monthly reducible terms for various periods.
| Amount borrowed |
2 years |
3 years |
4 years |
5 years |
| $12,000 |
$269 |
$190 |
$141 |
$127 |
| $16,000 |
$358 |
$252 |
$201 |
$170 |
| $20,000 |
$427 |
$316 |
$251 |
$212 |
| $24,000 |
$536 |
$379 |
$301 |
$254 |
| $28,000 |
$581 |
$411 |
$326 |
$275 |
| $30,000 |
$679 |
$474 |
$376 |
$317 |
Assume there are 26 fortnights in each year.
(i) Will borrows $28,000 over 5 years. How much interest will he pay?
(ii) How much more interest will Will pay if he takes out a $12,000 loan for 5 years instead than a $12,000 loan for 2 years?
(iii) If Will takes out a loan for $24,000 for 2 years, will he pay twice the amount of interest than if he took out a $12,000 loan for 2 years?
Answer.(i) Total repayment = $37,750 so after repaying $28,000 he pays $7,750 in interest.
(ii) $14,510 - $1,988 = $2,522 more.
(iii) The 4 year amount is $27,822 against $13,988 - so not quite twice. |
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