Luke deposits $3,500 into each of two savings accounts.
Account I earns 3% annual simple interest.
Account II earns 3% interest compounded annually.
Luke does not make any additional deposits or withdrawals. What is the sum of the balances of Account I and Account II at the end of 4 years?
Responses
A $7,859.28
B $3,920.00
C $3,939.28
D $4,359.28
To solve this problem, we need to calculate the balance in each account after 4 years.
In Account I, the interest is simple, so the balance after 4 years is:
Initial deposit + (interest rate * initial deposit * time)
Account I balance = $3,500 + (0.03 * $3,500 * 4)
Account I balance = $3,500 + (0.03 * $14,000)
Account I balance = $3,500 + $420
Account I balance = $3,920
In Account II, the interest is compounded annually, so the balance after 4 years is:
Balance after 4 years = initial deposit * (1 + interest rate)^time
Account II balance = $3,500 * (1 + 0.03)^4
Account II balance = $3,500 * (1.03)^4
Account II balance = $3,500 * (1.1255)
Account II balance = $3,939.25
The sum of the balances in Account I and Account II is:
$3,920 + $3,939.25 = $7,859.25
Therefore, the correct response is A) $7,859.28.