Suppose you invest $1600 at an annual interest rate of 7.9% compounded continuously. How much will you have in the account after 10 years?
A. $35,254.34
B. $3,525.43
C. $3,435.91
D. $17,315.27
B = P*e^(Yr)
where B is balance, P is principle = 1600; e is the number e; Y is the number of years; and r is the rate 0.079
Plug these numbers in and solve for the answer.
To find out how much money you will have in the account after 10 years with continuous compounding, you can use the formula:
A = P * e^(rt)
where:
A is the final amount
P is the principal amount (initial investment)
e is the base of the natural logarithm (approximately 2.71828)
r is the interest rate
t is the time in years
Let's plug in the values from the question:
P = $1600
r = 7.9% or 0.079 (convert the interest rate to decimal form)
t = 10 years
A = 1600 * e^(0.079 * 10)
Now we can calculate the result using a calculator with the exponential function (e^x):
A ≈ 1600 * e^0.79
A ≈ 1600 * 2.2033967
A ≈ 3525.4352
Therefore, you will have approximately $3525.44 in the account after 10 years.
The correct answer is B. $3,525.43.