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?

Answer 1

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.