Final answer:
To find out how much money is in the savings account on Karen's 4th birthday, we need to calculate the compound interest earned each year. The answer is $3,200.
Step-by-step explanation:
To find out how much money is in the savings account on Karen's 4th birthday, we need to calculate the compound interest earned each year.
On the day she is born, her grandparents deposit $2,000 into the account.
Each year, her parents add an additional $750 into the account.
The formula to calculate compound interest is A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the principal amount is $2,000 + $750 = $2,750.
The annual interest rate is 2.5% = 0.025, and the interest is compounded once per year.
Substituting the values into the formula, we get A = $2,750(1 + 0.025)^(4).
Calculating the expression inside the parentheses, we get 1.025^4 = 1.103809.
Multiplying that by the principal amount, we get A = $2,750 * 1.103809 = $3,034.47.
Therefore, the answer is option (b) $3,200.