Everything Maths Grade 12

4.4 CHAPTER 4. FINANCE

n = 30× 12 = 360 months

i = 0, 075 ÷ 12 = 0, 00625

Step 3 : Solve the problem

R960 000 =

x[1− (1 + 0,00625)−^360 ]

0 , 00625

= x(143,0176273)

x = R6 712, 46

Step 4 : Write the final answer

The monthly repayments =R6 712, 46

Exercise 4 - 2

1. A property costs R1 800 000. Calculate the monthlyrepayments if the interest rate is 14% p.a.
   compounded monthly and the loan must be paid off in 20 years time.


2. A loan of R 4 200 is to be returned in twoequal annual instalments. If the rate of interest of 10%
   per annum, compounded annually, calculate theamount of each instalment.

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(1.) 01e3 (2.) 01e4

Calculating Capital Outstanding EMCAL

As defined in Section 4.4.1, capital outstandingis the amount we still owe the people we borrowed
money from at a given moment in time. We alsosaw how we can calculate this using loan schedules.
However, there is a significant disadvantage to this method: it is very timeconsuming. For example, in
order to calculate how much capital is still outstanding at time 12 using the loan schedule, we’ll have
to first calculate how much capital is outstandingat time 1 through to 11 as well. This is alreadyquite
a bit more work than we’d like to do. Can youimagine calculating theamount outstanding after 10
years (time 120 )?

Fortunately, there is aneasier method. However, it is not immediatelyclear why this works, solet’s
take some time to examine the concept.

Prospective Method forCapital Outstanding

Let’s say that after a certain number of years, just after we made a repayment, we still owe amount Y.
What do we know about Y? We know that using the loan schedule, we can calculate what it equals
to, but that is a lot of repetitive work. We also know that Y is the amount that we are still going to pay