George deposits $2,500 into each of two savings accounts.
Account I earns 4.5% annual simple interest.
Account II earns 4.5% interest compounded annually.
George 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?
$5931.30
$3374.65
$2924.00
$900.00
To calculate the balance of Account I after 4 years with simple interest, we use the formula:
A = P(1 + rt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
t = number of years the money is deposited for
For Account I:
P = $2,500
r = 0.045
t = 4
A = $2,500(1 + 0.045*4)
A = $2,500(1 + 0.18)
A = $2,500(1.18)
A = $2,500 * 1.18
A = $2950
The balance of Account I after 4 years with simple interest is $2,950.
To calculate the balance of Account II after 4 years with compound interest, we use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years the money is deposited for
For Account II:
P = $2,500
r = 0.045
n = 1 (compounded annually)
t = 4
A = $2,500(1 + 0.045/1)^(1*4)
A = $2,500(1 + 0.045)^4
A = $2,500(1.045)^4
A = $2,500(1.194773)
A = $2,987.93
The balance of Account II after 4 years with compound interest is $2,987.93.
Therefore, the sum of the balances of Account I and Account II at the end of 4 years is $2,950 + $2,987.93 = $5,937.93
So the correct answer is $5931.30.