Question

An initial amount of $2300 is invested in an account at an interest rate of 3.5% per year, compounded continuously. Assuming that no withdrawals are made,

find the amount in the account after three years.
Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

Answer: To find the amount in the account after three years with continuous compounding, we use the formula for continuous compound interest:

A = P * e^(rt),

where:

A = the amount after time t,

P = the principal amount (initial investment),

e = the mathematical constant (approximately 2.71828),

r = the interest rate per year (in decimal form),

t = the number of years.

In this case:

P = $2300,

r = 3.5% = 0.035 (as a decimal),

t = 3 years.

Now, plug the values into the formula:

A = $2300 * e^(0.035 * 3).

Calculate the amount:

A = $2300 * e^(0.105) ≈ $2300 * 1.111483.

A ≈ $2558.363 (rounded to six decimal places).

So, the amount in the account after three years with continuous compounding is approximately $2558.36.