| Finding a repayment amount. |
1. (i) Develop an expression for the amount Louise and Nigel owe at the end of the 2nd month.
See below.
(ii) Hence calculate the value of the monthly installments $P.
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2. (i) 
NOTE: Here I have divided the rate by 52 to get 0.0067 (to add to the 1).
I could have used r to represent the rate and then used r = in my calculator. Same result. Make sure if you use that approach you use at least (say) 4 decimal places.
(ii) If David had continued to save, the car would have been sold and he would be waiting several years more to save that amount. In this case, David is advised to borrow but not take on other debt as well. |
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3. 
Note: The 106 to write millions of dollars was omitted because unnecessary so the answer is multiplied by 106 to obtain the correct magnitude for the repayment. |
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4. (i) 
(ii) 
(iii) Amount repaid = 20 × 611.57 = $12,231.40
∴ interest was $2,231.40. |
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5. (i) 
(ii) Interest = 52 × $40.86 - $2000 = $125.72.
(iii)
(v) At the end of 48 weeks, the balance has risen to $1,086.28
(simply replace the index of 2 in the last equation with 22
(48 - 26) = 22.
The problem with the increasing balance is that the extra expenditure of $50 also attracts interest but the repayment is only matching the expenditure and not the interest. Hence the balance increases each week.
So Charlotte's strategy is not a good financial decision. |
| Finding the amount to be borrowed. |
6.  |
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7.  |