6.6 CHAPTER 6. FINANCE
A = P(1 + i× n) (6.5)Solving for P gives:
P =A
(1 + i× n)(6.6)
Let us say you need toaccumulate an amountof R1 210 in 3 years time, and abank
account pays simple interest of 7%. How much would you need to invest in thisbank
account today?P =
A
1 + n. i
=R1 210
1 + 3× 7%
= R1 000
Does this look familiar?Look back to the simpleinterest worked example in Grade 10.
There we started with anamount of R1 000 and looked at what it would grow to in 3 years’
time using simple interest rates. Now we have worked backwards to seewhat amount we
need as an opening balance in order to achievethe closing balance of R1 210.In practise, however, present values are usuallyalways calculated assuming compound interest. So
unless you are explicitlyasked to calculate a present value (or opening balance) using simple interest
rates, make sure you usethe compound interest rate formula!Exercise 6 - 3
- After a 20-year period Josh’s lump sum investment matures to an amount of R313 550. How
much did he invest if hismoney earned interest at a rate of 13 ,65% p.a. compounded half yearly
for the first 10 years, 8 ,4% p.a. compounded quarterly for the next fiveyears and 7 ,2% p.a.
compounded monthly for the remaining period? - A loan has to be returned in two equal semi-annual instalments. If the rate of interest is 16% per
annum, compounded semi-annually and each instalment is R1 458, find the sum borrowed.
More practice video solutions or help at http://www.everythingmaths.co.za(1.) 017r (2.) 017s6.6 Findingi EMBX
By this stage in your studies of the mathematicsof finance, you have always known what interestrate
to use in the calculations, and how long the investment or loan will last. You have then eithertaken
a known starting point and calculated a future value, or taken a knownfuture value and calculated a
present value.
But here are other questions you might ask:- I want to borrow R2 500 from my neighbour, who said I could pay back R3 000 in 8 months
time. What interest is she charging me?