Question

A woman wishes to deposit a lump sum into a savings account now from which she can withdraw regular amounts to pay for her maintenance of her motor car. She will need to withdraw regular half yearly amounts from the savings account starting with a withdrawal of R1500 18 months from now and with a last withdrawal 5 years from now. To keep up with inflation the withdrawals will need to increase at a rate of 6% p.a each half year starting from the second withdrawal onwards. If the savings account earns interest at a rate of 6.8 p.a compounded daily then the amount that must be in the savings account is equal?

Answer 1

find the rate taking into account inflation

$i=(1+i)\times\sqrt[4.5]{i}-1=(1+0.068)\times\sqrt[4.5]{0.06}-1=4.2862=4.29$

$FVA1=1500\times\frac{(1+\frac{0.068}{2})^{1}-1}{\frac{0.068}{2}}\times(1+\frac{0.068}{2})=1551$

$FVA2=1551\times\frac{(1+\frac{0.0429}{2})^{9}-1}{\frac{0.0429}{2}}\times(1+\frac{0.0429}{2})=15545.04$

FVA=FVA1+FVA2=1 551+15 545.04=17 096.04