Natalie invested $1,200 in an account paying an interest rate of 6.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 17 years?
The formula for calculating the amount of money in an account with continuously compounded interest is given by the formula:
A = P * e^(r * t)
Where:
A = the final amount of money in the account
P = the principal amount of money invested
r = the annual interest rate (expressed as a decimal)
t = the time in years
Plugging in the given values:
A = 1200 * e^(0.064 * 17)
Calculating this using a calculator or computer program, we find:
A ≈ 1200 * 2.71828^(0.064 * 17) ≈ 1200 * 2.71828^(1.088) ≈ 1200 * 2.963 ≈ $3556
Therefore, the amount of money in the account after 17 years would be approximately $3,556.