Answer to Question #215225 in Financial Math for Nanah

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

Answer 1

The interest rate i=10% =0.1

Yearly payment = R3600

Yearly growth = R360

Growth % = 10% = 0.1

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

$FV = PMT \times n(1+i)^{n-1}(1+iT)$

PMT = the initial payment

PMT=R3600

n= the total period

n=20

i= the interest rate

i=10% = 0.1

T=1, if payment made in the beginning of each period

$FV = 3600 \times 20 \times (1+0.1)^{20-1}(1+0.1) \\ = 7200 \times 1.1^{19} \times 1.1 \\ = 484379.99$