Cynthia deposits $1,800 into each of two savings accounts.
Account I earns 5% annual simple interest.
Account II earns 5% interest compounded annually.
Cynthia 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 7 years?
$1,362.78
$4,962.78
$6,300.00
$3,202.38
To calculate the balance of Account I after 7 years with simple interest, we can use the formula:
A = P(1 + rt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (the initial amount of money)
r = annual interest rate (as a decimal)
t = time the money is invested for in years
For Account I:
P = $1800
r = 0.05
t = 7
A = $1800(1 + 0.05*7)
A = $1800(1 + 0.35)
A = $1800(1.35)
A = $2430
So, the balance of Account I after 7 years with simple interest is $2430.
To calculate the balance of Account II after 7 years with compound interest, we can 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 (the initial amount of money)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time the money is invested for in years
For Account II:
P = $1800
r = 0.05
n = 1 (since it is compounded annually)
t = 7
A = $1800(1 + 0.05/1)^(1*7)
A = $1800(1.05)^7
A = $1800(1.407036)
A = $2533.66
So, the balance of Account II after 7 years with compound interest is $2533.66.
The sum of the balances of Account I and Account II at the end of 7 years is:
$2430 + $2533.66 = $4963.66
Therefore, the correct answer is $4,963.66.