Hudson invested $8,400 in an account paying an interest rate of 5.4% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 13 years?
We can use the formula for compound interest, given by the equation:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
Plugging in the values we know:
P = $8,400
r = 5.4% = 0.054
n = 4 (compounded quarterly)
t = 13
A = 8400(1 + 0.054/4)^(4*13)
A ≈ 8400(1.0135)^(52)
A ≈ 8400(1.9644)
Calculating the final value:
A ≈ $16,503.36
Therefore, to the nearest ten dollars, there would be $16,500 in the account after 13 years.