Answer:
To find the total interest earned by the account after 25 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the total amount after t years
P = the principal (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $2,750, r = 0.0325, n = 1 (compounded yearly), and t = 25. Plugging these values into the formula, we get:
A = 2,750(1 + 0.0325/1)^(1*25)
A = 2,750(1.0325)^25
A = 2,750(2.0154)
A = $5,534.85
To find the total interest earned, we need to subtract the initial deposit from the total amount:
Interest = $5,534.85 - ($2,750 x 25)
Interest = $5,534.85 - $68,750
Interest = $-63,215.15
This result indicates that the account holder would have lost money over the 25-year period, as the interest earned was not enough to offset the annual deposits. However, it's worth noting that this calculation assumes no additional deposits or withdrawals were made during the 25 years. If the account holder had made additional deposits or withdrawals, the total interest earned would be different.