Today, Jan. 1, 2023, Nick starts an investment account and this account guarantees an interest rate of 6%, compounded monthly.

To start, he first transfers his $3,000 saving into this account so the account balance is $3,000 on Jan. 1, 2023 (t= month 0). In addition, he will continue to add money to this account through two ways for totally 5 years.

First, at the end of each month, he will deposit $500 from his earnings to this account. First $500 will be deposited on Jan. 31, 2023 (t=1) and last deposit of $500 will be made on Dec. 31, 2027 (t=60), totally 60 monthly deposits ($500 each).

Second, his grandparents will transfer $3,000 to this account once every 6 months. First transfer will be made on June 30, 2023 (t=6) and last transfer will be made on Dec. 31, 2027 (t=60), totally 10 transfer payments ($3,000 each).

In addition, the financial institute which manages this account will charge monthly management fee and this fee will be deducted from the account at the end of each month. The fee for the first month (deducted on Jan. 31, 2023) will be $10 and this fee is going to increase by $1 per month thereafter. Therefore, the management fee for the last month of the 5-year period (Dec. 31 2027) will be $69.

Find how much will be accumulated at the end of Dec. 31, 2027?