Question

a. What is the future value in six years of $1,400 invested in an account with an annual percentage rate of 9 percent, compounded annually? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future value $  

b. What is the future value in six years of $1,400 invested in an account with an annual percentage rate of 9 percent, compounded semiannually? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future value $  

c. What is the future value in six years of $1,400 invested in an account with an annual percentage rate of 9 percent, compounded monthly? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future value $  

d. What is the future value in six years of $1,400 invested in an account with an annual percentage rate of 9 percent, compounded continuously? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future value $   

Answer 1

Solution a:

Principal amount = $1,400

rate of interest = 9% compounded annually

Period = 6 years

Future value = P (1+r)^t = $1,400 (1+0.09)^6 = $1,400 * 1.6771 = $2,347.94

Solution b:

Principal amount = $1,400

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 = $1,400 * 1.6959 = $2,374.23

Solution c:

Principal amount = $1,400

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 = $1,400 (1+0.0075)^72 = $1,400 * 1.7125 = $2,397.50

Solution d:

Principal amount = $1,400

Rate of interest = 9% compounded continuously

Period = 6 years

Future value = P * e^rt = $1,400 (2.71828)^(0.09*6) = $1,400 * 1.7160 = $2,402.40