Calculating an outstanding balance

Question

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

Comments

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. 

Answer 1

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.

Comments

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.

Answer 2

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.