<< Chapter < Page | Chapter >> Page > |
By this stage in your studies of the mathematics of finance, you have always known what interest rate to use in the calculations, and how long the investment or loan will last. You have then either taken a known starting point and calculated a future value, or taken a known future value and calculated a present value.
But here are other questions you might ask:
Each time that you see something different from what you have seen before, start off with the basic equation that you should recognise very well:
If this were an algebra problem, and you were told to “solve for $i$ ", you should be able to show that:
You do not need to memorise this equation, it is easy to derive any time you need it!
So let us look at the two examples mentioned above.
Note that in both examples, we expressed $n$ as a number of years ( $\frac{8}{12}$ years, not 8 because that is the number of months) which means $i$ is the annual interest rate. Always keep this in mind - keep years with years to avoid making silly mistakes.
By this stage you should be seeing a pattern. We have our standard formula, which has a number of variables:
We have solved for $A$ (in Grade 10), $P$ (in "Present Values or Future Values of an Investment or Loan" ) and $i$ (in "Finding i" ). This time we are going to solve for $n$ . In other words, if we know what the starting sum of money is and what it grows to, and if we know what interest rate applies - then we can work out how long the money needs to be invested for all those other numbers to tie up.
This section will calculate $n$ by trial and error and by using a calculator. The proper algebraic solution will be learnt in Grade 12.
Solving for $n$ , we can write:
Now we have to examine the numbers involved to try to determine what a possible value of $n$ is. Refer to your Grade 10 notes for some ideas as to how to go about finding $n$ .
We invest R3 500 into a savings account which pays 7,5% compound interest for an unknown period of time, at the end of which our account is worth R4 044,69. How long did we invest the money?
We are required to find $n$ .
We know that:
We now use our calculator and try a few values for $n$ .
Possible $n$ | $1,{075}^{n}$ |
1,0 | 1,075 |
1,5 | 1,115 |
2,0 | 1,156 |
2,5 | 1,198 |
We see that $n$ is close to 2.
The R3 500 was invested for about 2 years.
Notification Switch
Would you like to follow the 'Siyavula textbooks: grade 11 maths' conversation and receive update notifications?