Nathan invested $3,500 in an account paying an interest rate of 3.5% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 19 years?
The formula to calculate the future value of an investment with compound interest is:
\[A = P\left(1 + \frac{r}{n}\right)^{nt}\]
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested
In this case, P = $3,500, r = 0.035 (3.5% expressed as a decimal), n = 4 (quarterly compounding), and t = 19 years.
Plugging in these values, we get:
\[A = 3500\left(1 + \frac{0.035}{4}\right)^{4(19)}\]
Let's compute this using a calculator.