You invest $4000 in an account paying 4.1% continuously compounded interest. How much will you have in 8 years
4000 * e^(rt)
4000 * e^.328
To calculate how much you will have in 8 years with continuous compounding, you can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A is the amount of money accumulated after time t
P is the principal (initial investment)
e is the mathematical constant approximately equal to 2.71828
r is the interest rate (in decimal form)
t is the time period in years
In this case, the principal (P) is $4000, the interest rate (r) is 4.1% (or 0.041), and the time period (t) is 8 years.
Plugging in these values into the formula, we get:
A = 4000 * e^(0.041 * 8)
To calculate this, you can use a calculator or a math software that can perform exponentiation and evaluate the constant 'e'. For example, using a calculator, the calculation can be done as follows:
A ≈ 4000 * 2.71828^(0.041 * 8)
A ≈ 4000 * 2.71828^(0.328)
A ≈ 4000 * 1.3881
A ≈ 5552.40
Therefore, you will have approximately $5,552.40 in 8 years with continuous compounding interest.