Dan and Sara open two separate funds. Dan's fund accumulates according to compound interest with an annual effective interest rate of $2i.$ Sara's fund accumulates according to simple interest with an annual effective interest rate of i$.$ Dan makes an opening deposit of $1000$ while Sara makes an opening deposit of $3000.$ The amount of interest earned in the fourth year for Dan's fund is equal to the amount of interest earned in the fourth year for Sara's fund. Calculate the total amount of interest earned in Dan's fund over the first four years.