A loan of $$1475$ taken out on June $7$ requires three payments. The first payment is due on July $7.$ The second payment is twice as large as the first payment and is due on August $19.$ The final payment due on November $2$ is three times as large as the first payment. If the focal date is June $7,$ what is the size of each of the three payments at an interest rate of $4\mathrm{.}6\%?$