Like 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?
a $7,859.28
b $3,920.00
c $3,939.28
d $4,359.28
For Account I, the interest earned after 4 years would be $3,500 * 0.03 * 4 = $420.
Therefore, the balance of Account I after 4 years would be $3,500 + $420 = $3,920.
For Account II, we can use the compound interest formula: A = P(1 + r/n)^(nt), where:
A is the final amount
P is the principal (initial amount)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
and t is the number of years.
In this case, P = $3,500, r = 0.03, n = 1 (compounded annually), and t = 4 years.
Using the formula, A = $3,500(1 + 0.03/1)^(1*4)
A = $3,500(1 + 0.03)^4
A = $3,500(1.03)^4
A ≈ $3,939.28
So, the sum of the balances of Account I and Account II at the end of 4 years is $3,920 + $3,939.28 = $7,859.28.
The correct answer is a) $7,859.28.