marques invested $13,000 in an account paying an interest rate of 2.2% compounded continuously. assuming no…
marques invested $13,000 in an account paying an interest rate of 2.2% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 16 years?
Answer
Explanation:
Step1: Identify the formula
The formula for continuous compounding is (A = Pe^{rt}), where (A) is the final amount, (P) is the principal amount, (r) is the annual interest rate (in decimal form), and (t) is the time in years.
Step2: Convert the interest rate to decimal
Given (r = 2.2%=0.022), (P = 13000), and (t = 16).
Step3: Substitute the values into the formula
Substitute (P = 13000), (r = 0.022), and (t = 16) into (A=Pe^{rt}), we get (A = 13000\times e^{0.022\times16}). First, calculate (0.022\times16 = 0.352). Then (A = 13000\times e^{0.352}). Since (e^{0.352}\approx1.4216) (using a calculator for the exponential function).
Step4: Calculate the final amount
(A=13000\times1.4216 = 18480.8)
Answer:
(18480.80)