Everything Maths Grade 12

4.3 CHAPTER 4. FINANCE

Example 1: Term of Investment - Logarithms

QUESTION

Suppose we invested R3 500 into a savings account which pays 7 ,5% compound interest. After

an unknown period of time our account is worth R4 044, 69. For how long did weinvest the

money? How does thiscompare with the trial and error answer from Chapter ??.

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

(1 +i)n = (A/P )

log((1 +i)n) = log(A/P )

n log(1 +i) = log(A/P )

n = log(A/P )/ log(1 +i)

Step 3 : Solve the problem

n = log(A/P )/ log(1 +i)

=

log(^40443500 ,^69 )

log(1 + 0.075)

Remember that: 7 .5% =

7. 5

100

= 0. 075

= 2. 0

Step 4 : Write final answer

The R3 500 was invested for 2 years.

4.3 Series of Payments.

By this stage, you knowhow to do calculationssuch as ‘If I want R1 000 in three years’ time, how

much do I need to invest now at 10%?’

What if we extend this as follows: “If I want to draw R1 000 next year, R1 000 the next year and R1 000