The amount of money A in an account after t years of investing a principal P at a rate r compounded continuously, is:
[tex]A=Pe^{rt}[/tex]To find the value P that he must pay now so that the amount of money will be equal to $5000 in 6 years at a rate of 2.5% per year, isolate P and substitute A=5000, r=2.5/100 and t=6:
[tex]\begin{gathered} \Rightarrow P=\frac{A}{e^{rt}}=Ae^{-rt} \\ \Rightarrow P=5000\cdot e^{-\frac{2.5}{100}\times6} \\ =5000\cdot e^{-0.025\times6} \\ =5000\cdot e^{-0.15} \\ =4303.53988\ldots \\ \approx4303.54 \end{gathered}[/tex]Therefore, he paid $4303.54.
