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?

Answer 1

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.