A $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account?
(1 point)
Responses
$500,000.00
$500,000.00
$4,862.03
$4,862.03
$4,600.00
$4,600.00
$20,250.00
To find the balance in the account after 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final balance in the account
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the principal (P) is $4,000.00, the annual interest rate (r) is 5% (or 0.05 as a decimal), the number of times interest is compounded per year (n) is 1 (compounded annually), and the number of years (t) is 4.
Plugging these values into the formula:
A = $4,000.00(1 + 0.05/1)^(1*4)
A = $4,000.00(1 + 0.05)^4
A = $4,000.00(1.05)^4
A = $4,000.00(1.21550625)
A = $4,862.03
Therefore, the balance in the account after 4 years is $4,862.03.
The correct answer is $4,862.03.