Question

Joseph invested $16,000 in an account paying an interest rate of 5.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 14 years?

Answer 1

Okay, let's solve this step-by-step:

* Joseph invested $16,000 at an interest rate of 5.7% compounded continuously

* We need to calculate the balance after 14 years

* Formula for continuous compounding:

A = Pe^rt

Where:

A = Final Amount

P = Principal Amount

e = Euler's number (approximately 2.71828)

r = Interest rate (in decimal form)

t = Time in years

* Plugging in the values:

A = 16,000e^(0.057*14)

A = 16,000e^0.798

A = 16,000 x 2.22

A = $35,520

* Rounding to the nearest cent, the amount after 14 years is $35,520.00

Therefore, the amount of money in the account to the nearest cent after 14 years is $35,520.00