Question

If $4000 is invested at an interest rate of 9.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)

a) 4000e0.0925t
b) 4000(1+0.0925)t
c) 4000(1+0.0925/t)t
d) 4000(1+0.0925t/t)

Answer 1

The value of the investment after a given number of years can be found using the continuous compound interest formula: A = P * e^(rt), where A is the final value, P is the principal amount, e is the base of the natural logarithm, r is the interest rate, and t is the number of years.

Step-by-step explanation:

In this case, the value of the investment after a given number of years can be found using the continuous compound interest formula: A = P * e^(rt), where A is the final value, P is the principal amount, e is the base of the natural logarithm (approximately 2.71828), r is the interest rate, and t is the number of years.

To find the value of the investment after a given number of years, substitute the given values into the formula. In this case, the principal amount is $4000, the interest rate is 9.25% per year, and the number of years is t. So the answer is $4000e^(0.0925t).