Question

Suppose you invest $1,600 for six years at an annual percentage rate of 9 percent. a. What is the future value if interest is compounded annually? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the future value if interest is compounded semiannually? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What is the future value if interest is compounded monthly? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. What is the future value if interest is compounded continuously? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a. Principal amount = $1,600

rate of interest = 9% compounded annually

Period = 6 years

Future value = P (1+r)^t

= $1,400 (1+0.09)^6

= $1,600 * 1.6771

= $2683.36

b. Principal amount = $1,600

rate of interest = 9% compounded semi annually, semi annual rate of interest = 9*6/12 = 4.5%

Time = 6 years, semiannual period = 6*2 =12

Future value = P (1+r)^t = $1,400 (1+0.045)^12

= $1,600 * 1.6959

= $2713.44

c. Principal amount = $1,600

Rate of interest = 9% compounded monthly, monthly rate of interest = 9/12 = 0.75%

Time = 6 years, monthly period = 6*12 =72

Future value = P (1+r)^t

= $1,600 (1+0.0075)^72

= $1,600 * 1.7125

= $2740

d. Principal amount = $1,400

Rate of interest = 9% compounded continuously

Period = 6 years

Future value = P * e^rt

= $1,600 (2.71828)^(0.09*6)

= $1,600 * 1.7160

= $2745.60