Jennifer invested $2,500 in an account earning 3.5% interest compounded continuosly. How much money will she have in the account after 15 years?
continuous growth is given by the equation
amount = initial e^ (rt) , where r is the annual rate expressed as a decimal
amount = 2500 e^(15(.035))
= 4226.15
( compare that with the amount had it been 3.5% per annum compounded annually
amount = 2500(1.035)^15 = 4188.37 )
To calculate the final amount Jennifer will have in the account after 15 years with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = the final amount
P = the principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = annual interest rate (as a decimal)
t = time in years
In this case, Jennifer invested $2,500, the interest rate is 3.5% (0.035 as a decimal), and the time is 15 years. Let's plug these values into the formula:
A = 2500 * e^(0.035 * 15)
To find the final amount, we first need to calculate the exponential term:
e^(0.035 * 15) ≈ 1.62745
Now, we can calculate the final amount:
A = 2500 * 1.62745
A ≈ $4,068.63
Therefore, Jennifer will have approximately $4,068.63 in the account after 15 years.