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Financial Mathematics

1. A photocopying machine is bought at a cost of R45 000.
1.1. If the current model will be replaced in 4 years time, how much will the new machine cost if the inflation rate is 11,5% p.a. ? (Round off to the nearest ten rand).
1.2. If the machine depreciates at a rate of 9,25% p.a., how much will it be worth in 4 years time? (Round off to the nearest ten rand).

SOLUTION
1.1. Write down what you know!

Compound Interest Formula;
P = 45 000
i = 11,5%
n = 4
A = ???

Now substitute into the following formula:

To the nearest 10 rand:
R69 550

1.2. Compound Decay Formula:
P = 45 000
i = 9,25%
n = 4
A = ???

Answer to the nearest ten rand:
R 30 520

2. A shopkeeper invested an inheritance into a pension fund over a period of 10 years. The fund grew to R75 000 after an initial investment of R25 000.
Calculate the interest rate per annum compounded annually that will yield the same return.

Again, write down what you know!

A = R75 000
P = R25 000
n = 10
i = ???

Thus...
1,116123…= 1 + i
0,116.. = i

Therefore
i = 11,6% p.a.