A $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account?%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A$500,000.00%0D%0A$500,000.00%0D%0A%0D%0A$4,862.03%0D%0A$4,862.03%0D%0A%0D%0A$4,600.00%0D%0A$4,600.00%0D%0A%0D%0A$20,250.00%0D%0A$20,250.00
The correct answer is $4,600.00.
To calculate the balance after 4 years, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case:
P = $4,000.00
r = 5% or 0.05 (decimal value)
n = 1 (annual compounding)
t = 4 years
Plugging in these values, we have:
A = 4000(1 + 0.05/1)^(1*4)
A = 4000(1 + 0.05)^4
A = 4000(1.05)^4
A = 4000(1.21550625)
A = $4,862.03 (rounded to the nearest cent)
Therefore, the balance in the account after 4 years is $4,862.03.