If you'd like to upgrade your subscription, your current subscription will end immediately. In its place your new subscription will begin, continuing a number of days that are equal in price to the unused period of your old subscription. At the moment of the upgrading, no additional fees are taken. The recurring payment will occur monthly after this prorated period ends.
There are three kinds of subscriptions in the game: Silver monthly subscription (~$5), Golden monthly subscription (~$15), and Golden weekly subscription (~$5).
You currently have subscribed to a Silver monthly subscription on April 1.
On April 15, you chose to upgrade Silver monthly subscription to the Golden monthly subscription, which costs ~$15 per month.
Your Silver subscription ends immediately. Since you paid for a full month (April 1-30) but upgraded halfway through the subscription period, half of a month's subscription (~$2.5) is applied to your new subscription. However, since that new subscription costs ~$15 per month, the $2.5 credit balance pays for only 5 days (April 16-21), so on April 22, you will be charged ~$15 for a new subscription and another ~$15 on the 22nd of each month following.
Prices can vary in the game due to currency exchange rates. We included them here just as an example.