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Calculating an outstanding balance

+1 vote
asked May 11, 2017 in BUS 1003H - Introduction to Financial Risk by scksan001 (180 points)

The question is posted below.

How does one go about answering #2 of this question? I tried calculating the difference between the R10 000 and the outstanding balance after 6 savings but it was wrong. I also tried a few other methods but can't get the answer.

Answers given in the solutions: 

1)  7 years

2)  R603.74


commented May 12, 2017 by Abigail Vigar (640 points)

Thanks Zaba. 

Don't stress too much about this question. Loans has been taken out from this course so this question is a little bit beyond the scope of this course. All you need to know about loans is what you covered in class with Sure. 

2 Answers

+1 vote
answered May 12, 2017 by Zaba_Mvelase (570 points)
selected May 15, 2017 by Rowan
Best answer

The future value of the 1st 6 annual R1000 investments at time 6 is $$1000\ddot{a} \bar{6|} = 8487.14$$ The future value of this amount to time 7 is therefore $$8487.171 * (1.1)^1 = 9335.89$$ This means that the amount he needs to invest at the beginning of the final year is $$(10000 - 9335.89) * (1.1)^{-1} = 603.738$$ This is just 1 way of answering the question.

commented May 12, 2017 by Zaba_Mvelase (570 points)

For example, you could also answer the question in the following way: the value of the investment at time 6 (end of the 6th year which is the same as the start of the 7th year) is 8487.17. This means that \(8487.17 + x \) should give you a total investment value of 10 000 when accumulated to the end of the 7th year (x is the final savings amount he invests that is less than 1000) $$(8487.17 + x) * (1 + 10\%)^{1} = 10 000$$ Solving for x gives you 603.738 as well.

+1 vote
answered May 11, 2017 by Abigail Vigar (640 points)

There are a few ways to answer this question but since it has two parts it is probably best to use your answer in part #1. 

So when you worked out the 7 years you would have got a value more like 6..... that was then rounded up to get 7. Try using that original value and see if you can get the answer given.