An investment fund provides annual rates of return, which are independent and identically distributed, with annual accumulation factors following the log-normal distribution with mean 1.04 and variance 0.02. An investor knows that she will have to make a payment of 8,000 in five years' time. Calculate the amount of cash she should invest now in order that she has a 99% chance of having sufficient cash available in five years' time from the investment to meet the payment.