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Question
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$7,859.28
B $3,920.00$3,920.00
C $3,939.28$3,939.28
D $4,359.28
To find the balance of Account I after 4 years, we can use the formula for simple interest:
Balance = Principal + (Principal * interest rate * time)
For Account I, the principal is $3,500 and the interest rate is 3% per year (or 0.03). The time is 4 years.
Balance of Account I = $3,500 + ($3,500 * 0.03 * 4)
= $3,500 + ($420)
= $3,920
So the balance of Account I after 4 years is $3,920.
To find the balance of Account II after 4 years, we can use the formula for compound interest:
Balance = Principal * (1 + interest rate)^time
While the interest rate and time are the same as Account I, the principal for Account II is also $3,920 (as it is the balance of Account I after 4 years).
Balance of Account II = $3,920 * (1 + 0.03)^4
= $3,920 * (1.03)^4
= $3,920 * 1.1255
= $4,398.28
Therefore, the sum of the balances of Account I and Account II at the end of 4 years is $3,920 + $4,398.28 = $8,318.28, which is not listed as an option.
None of the provided options is the correct answer.
Are you sure?
Apologies for the mistake in the previous response. Let's recalculate the balances.
For Account I:
Balance = Principal + (Principal * interest rate * time)
Balance = $3,500 + ($3,500 * 0.03 * 4)
Balance = $3,500 + ($420)
Balance = $3,920
For Account II:
Balance = Principal * (1 + interest rate)^time
Balance = $3,500 * (1 + 0.03)^4
Balance = $3,500 * (1.03)^4
Balance = $3,500 * 1.1255
Balance = $3,939.25
So the sum of the balances of Account I and Account II at the end of 4 years is $3,920 + $3,939.25 = $7,859.25.
Therefore, the correct answer is option A, $7,859.28.