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.
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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
3 answers
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.
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.