To determine effective cost of investment

Question

I have this problem,need of help on how to attempt it. If you pay for a certain investment with installments of GCD 1000 in early January and GCD 1000 in early July and then receive GCD 2000 in late December of the same year,find the effective cost to you of this investment at the end of the period.Assume the risk free rate of interest is 3% per year.Assume continuous compounding of interest.Thanks

Answer 1

You need to move all the sums into the same time period, your question wants the value at the end of the year, so using $PV\cdot e^{rt}=FV$

Expenditure=$1000 e^{(.03)1}+1000e^{(.03)(.5)}\approx 2045.57$

Revenue=$2000$

So in end of the year dollars it costs you $45.57$