Everything Maths Grade 11

6.7 CHAPTER 6. FINANCE

6.7 Findingn — Trial and Error EMBY

By this stage you shouldbe seeing a pattern. Wehave our standard formula, which has a numberof

variables:

A = P .(1 + i)n

We have solved for A (in Grade 10), P (in Section 6.5) and i (in Section 6.6). 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. Theproper algebraic solution

will be learnt in Grade 12.

Solving for n, we can write:

A = P(1 + i)n

A

P

= (1 + i)n

Now we have to examine the numbers involvedto try to determine whata possible value of n is. Refer

to your Grade 10 notesfor some ideas as to howto go about finding n.

Example 5: Term of Investment —Trial and Error

QUESTION

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 accountis worth R4 044, 69. How long did we invest

the money?

SOLUTION

Step 1 : Determine what is given and what is required

• P =R3 500


• i = 7,5%


• A =R4 044, 69
  We are required to find n.

Step 2 : Determine how to approach the problem

We know that:

A = P(1 + i)n

A

P

= (1 + i)n