The man's account will be worth $9,144.63 after 7 years.
To calculate the future value of the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount invested ($6,900 in this case)
r = the annual interest rate (6.25% or 0.0625 as a decimal)
n = the number of times interest is compounded per year (monthly compounding, so n = 12)
t = the number of years the money is invested for (7 years in this case)
Plugging in the values into the formula, we get:
A = 6900(1 + 0.0625/12)^(12*7)
A = 6900(1 + 0.00520833333)^(84)
A = 6900(1.00520833333)^(84)
Using a calculator or spreadsheet, we can evaluate this expression to find:
A ≈ 9144.63
So, the man's account will be worth approximately $9,144.63 after 7 years.