jackson invested $8,200 in an account paying an interest rate of 4% compounded continuously. assuming no…

jackson invested $8,200 in an account paying an interest rate of 4% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 8 years?

jackson invested $8,200 in an account paying an interest rate of 4% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 8 years?

Answer

Explanation:

Step1: Identify the formula for continuous compounding

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 form

Given (r = 4%=0.04), (P=$8200), and (t = 8) years.

Step3: Substitute the values into the formula

Substitute (P = 8200), (r=0.04), and (t = 8) into (A = Pe^{rt}). So (A=8200\times e^{0.04\times8}). First, calculate (0.04\times8 = 0.32). Then (A = 8200\times e^{0.32}). Since (e^{0.32}\approx1.37712776) (using a calculator for the exponential function).

Step4: Calculate the value of (A)

(A=8200\times1.37712776\approx11292.45)

Answer:

(11292)