Jane invest a sum of money in a savings account with a fixed annual interest rate of 3.26% compounded countinuously. After 11 years, the balance reaches $7156.62. What was the amount of the initial investment

Answer: the amount of the initial investment is $5004.63

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

From the information given,

A = $7156.62

r = 3.26% = 3.26/100 = 0.0326

t = 11 years

Therefore

7156.62 = P x e (0.0326 x 11)

7156.62 = P x e (0.3586)

7156.62 = 1.43P

P = 7156.62 / 1.43

P = $5004.63