A $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account?
The formula to calculate the balance in the account after a certain number of years, with compound interest, is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $4,000.00
r = 5% = 0.05 (5% expressed as a decimal)
n = 1 (interest is compounded annually)
t = 4 (4 years)
Using the formula:
A = 4,000(1 + 0.05/1)^(1*4)
A = 4,000(1 + 0.05)^4
A = 4,000(1.05)^4
A = 4,000(1.21550625)
A = $4,862.03
Therefore, the balance in the account after 4 years is $4,862.03.