A loan of $$1600$ 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 $20.$ The final payment, due on November $4,$ 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 $4\mathrm{.}5\%?$

The first payment is $ $$ the second payment is $ $$ and the third payment is $ $$

$($Round the final answers to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$