# Calculating an outstanding balance

+1 vote
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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.

1)  7 years

2)  R603.74

commented May 12, 2017 by (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.

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

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.
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.