Answer to Question #197950 in Financial Math for Beauty Magadlela

Question

You are saving to pay for your children’s university costs in 20 years’ time. In the first year, your payment is R3 600, after which your yearly payments increased by R360 each year. If the expected interest rate per year is 10%, the amount that you expect to receive to the nearest rand on the maturity date will be

[1] R213 030.

[2] R340 380.

[3] R412 380.

[4] R484 380.

[5] none of the above. 

Answer 1

We need to calculate the future value of a growing annuity

Interest rate, i = 10%

Yearly payment = R3600

Yearly growth = R360

Growth % = 10%

Since growth and interest are same,the future value of a growing annuity is given by:

$FV = PMT ×n(1+i)^{n-1}(1+iT)$

PMT is the initial payment = R3600

n is the total period, = 20

i is the interest rate = 10%(0.1)

T=1 if payment is made at the beginning of each period

Future value will be:

$FV = 3600 × 20 ×(1+0.1)^{20-1}(1+0.1) = 72000 × 1.1^{19} ×1.1$

$FV =R 484379.99$

So option 4 is the correct answer.