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 solve this problem, we need to calculate the balance of Account I and Account II separately and then add them together.
For Account I, simple interest is calculated using the formula: I = P * r * t, where I is the interest, P is the principal, r is the interest rate, and t is the time.
For Account II, compound interest is calculated using the formula: A = P * (1 + r/n)^(n*t), where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the time.
For Account I:
Principal (P) = $3,500
Interest rate (r) = 3% = 0.03
Time (t) = 4 years
I = P * r * t = $3,500 * 0.03 * 4 = $420
The balance of Account I after 4 years will be the principal plus the interest: $3,500 + $420 = $3,920.
For Account II:
Principal (P) = $3,500
Interest rate (r) = 3% = 0.03
Number of times interest is compounded per year (n) = 1
Time (t) = 4 years
A = P * (1 + r/n)^(n*t) = $3,500 * (1 + 0.03/1)^(1*4) = $3,500 * (1.03)^4 ≈ $3,939.28
The balance of Account II after 4 years will be approximately $3,939.28.
The sum of the balances of Account I and Account II is $3,920 + $3,939.28 = $7,859.28.
Therefore, the correct answer is A) $7,859.28.