Question

a. Compute the future value of $2,500 continuously compounded for 5 years at an annual percentage rate of 9 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $ b. Compute the future value of $2,500 continuously compounded for 6 years at an annual percentage rate of 7 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $ c. Compute the future value of $2,500 continuously compounded for 9 years at an annual percentage rate of 4 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $ d. Compute the future value of $2,500 continuously compounded for 6 years at an annual percentage rate of 10 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $

Answer 1

The future value of the investments, calculated using continuous compounding at various interest rates and timelines, results in $3,926.75 for 9 percent over 5 years, $3,805.25 for 7 percent over 6 years, $3,580.50 for 4 percent over 9 years, and $4,555.25 for 10 percent over 6 years.

Step-by-step explanation:

To calculate the future value of an investment with continuous compounding, we use the formula FV = Pert, where P is the principal, e is the base of the natural logarithm (approximately equal to 2.71828), r is the annual interest rate (expressed as a decimal), and t is the time in years.

Calculations:

Make sure all calculations are done without rounding intermediate steps, but the final answers should be rounded to two decimal places.

Answer 2

Instructions are listed below.

Step-by-step explanation:

Giving the following information:

To calculate an investment that uses continuously compounded we need to use the following formula:

FV= P*e^(i*t)

A) Principal= 2,500

t= 5 years

i= 9%

FV= 2500*e^(0.09*5)= $3,920.78

B) P= 2,500

t= 6

i= 7%

FV= 2500*e^(0.07*6)= $3,804.90

C) P= 2,500

t= 9

i= 4%

FV= 2500*e^(0.04*9)= $3,583.32

D) P= 2,500

t= 6

i= 10%

FV= 2,500*e^(0.10*6)= $4,555.30