A $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account?
To find the balance after 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the ending balance
P = the principal (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case:
P = $4,000.00
r = 5% = 0.05
n = 1 (compounded annually)
t = 4
Plugging these values into the formula, we get:
A = 4000 * (1 + 0.05/1)^(1*4)
A = 4000 * (1 + 0.05)^4
A = 4000 * (1.05)^4
A = 4000 * 1.21550625
A ≈ 4862.03
The balance in the account after 4 years is approximately $4,862.03.