Final answer:
To calculate the total interest earned on the account, we can use the formula for compound interest. In this case, the total interest earned is approximately $1,181.33.
Step-by-step explanation:
To calculate the total interest earned on the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the final amount (including the principal and interest)
P is the principal (initial amount)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the time in years
In this case, the principal (P) is $49,080, the annual interest rate (r) is 2.61% or 0.0261, the compounding period (n) is 365 (since interest is compounded daily), and the time (t) is 229 days divided by 365 (approximately 0.6274 years).
Plugging in these values into the formula:
A = $49,080(1 + 0.0261/365)^(365*0.6274)
After evaluating this expression, we find that the total amount (A) is approximately $50,261.33.
To calculate the total interest earned, we subtract the principal (P) from the final amount (A):
Total interest earned = $50,261.33 - $49,080 = $1,181.33
Therefore, the total interest earned on the account after 229 days is approximately $1,181.33.