Question

Isaac wants his fiancee to make 14 half-yearly withdrawals starting now. He wants the first withdrawal to be R900, and subsequent withdrawals to increase by 9% every six months. Interest is earned at 8% pa compounded half-yearly.

How much will Isaac’s fiancee withdraw in total?

Answer 1

Since annual payments increase by 1.09 times (by 9%), the payments received to the account are a variable annuity with constant relative change of its members. Therefore, to assess the future value, we use the variable annuity formula:

$FV=900\times\frac{1.09^{14}-(1+\frac{0.08}{2})^{14}}{1.09-(1+\frac{0.08}{2})}=28 980.91$