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?

Answer 1

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.