Violet deposits $800 every quarter into an account earning an annual interest rate of 4.5% compounded quarterly. How much would she have in the account after 10 years, to the nearest dollar?
To calculate the amount of money Violet would have in the account after 10 years, we can 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 (the initial deposit or loan amount)
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 or borrowed for
In this case:
P = $800
r = 4.5% or 0.045
n = 4 (quarterly compounding)
t = 10 years
A = $800(1 + 0.045/4)^(4*10)
A = $800(1 + 0.01125)^40
A = $800(1.01125)^40
A = $800(1.5361)
A = $1,228.88
Therefore, Violet would have approximately $1,228 in the account after 10 years, to the nearest dollar.