Brian deposited $9,808 into a savings account that compounds interest on a daily basis, at a rate of 3.78%. If we want to find out how much interest he will earn after 12 years, we can use the formula:
A = P(1 + r/n)^(nt)
where A is the amount of money after t years, P is the principal amount (which is $9,808 in this case), r is the annual interest rate (3.78% in this case), n is the number of times the interest is compounded per year (which is 365 since it compounds daily), and t is the number of years (which is 12).
So, plugging in the values we get:
A = $9,808(1 + 0.0378/365)^(365*12)
A = $9,808(1.000103972)^4380
A = $9,808(1.496812899)
A = $14,682.54
Therefore, the interest Brian will earn after 12 years is $14,682.54 - $9,808 = $4,874.54. When we round this answer to the hundredths place, we get $4,874.54.